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We study static brane configurations in the bulk background of the topological black holes in asymptotically flat spacetime. We find that such configurations are possible even for flat black hole horizon, unlike the AdS black hole case. We construct the brane world model with an orbifold structure S^1/Z_2 in such bulk background. We also study massless bulk scalar field.
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arxiv:hep-th/0107174
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We analyze the dynamics of M-theory on a manifold of G_2 holonomy that is developing a conical singularity. The known cases involve a cone on CP^3, where we argue that the dynamics involves restoration of a global symmetry, SU(3)/U(1)^2, where we argue that there are phase transitions among three possible branches corresponding to three classical spacetimes, and S^3 x S^3 and its quotients, where we recover and extend previous results about smooth continuations between different spacetimes and relations to four-dimensional gauge theory.
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arxiv:hep-th/0107177
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We propose a superfield description of osp(1,2) covariant quantization by extending the set of admissibility conditions for the quantum action. We realize a superfield form of the generating equations, specify the vacuum functional and obtain the corresponding transformations of extended BRST symmetry.
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arxiv:hep-th/0107182
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We clarify the relation between the Dixmier-Douady class on the space of self adjoint Fredholm operators (`universal B-field') and the curvature of determinant bundles over infinite-dimensional Grassmannians. In particular, in the case of Dirac type operators on a three dimensional compact manifold we obtain a simple and explicit expression for both forms.
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arxiv:hep-th/0107207
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In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point functions, operator product expansions of logarithmic operators in arbitrary rank logarithmic conformal field theory are investigated. Since the precise relationship between logarithmic operators and their primary partners is not yet sufficiently understood in all cases, the derivation of operator product expansion formulae is only possible under certain assumptions. The easiest cases are studied in this paper: firstly, where operator product expansions of two primaries only contain primary fields, secondly, where the primary fields are pre-logarithmic operators. Some comments on generalization towards more relaxed assumptions are made, in particular towards the case where logarithmic fields are not quasi-primary. We identify an algebraic structure generated by the zero modes of the fields, which proves useful in determining settings in which our approach can be successfully applied.
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arxiv:hep-th/0107242
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We study the metrics on the families of moduli spaces arising from probing with a brane the ten and eleven dimensional supergravity solutions corresponding to renormalisation group flows of supersymmetric large n gauge theory. In comparing the geometry to the physics of the dual gauge theory, it is important to identify appropriate coordinates, and starting with the case of SU(n) gauge theories flowing from N=4 to N=1 via a mass term, we demonstrate that the metric is Kahler, and solve for the Kahler potential everywhere along the flow. We show that the asymptotic form of the Kahler potential, and hence the peculiar conical form of the metric, follows from special properties of the gauge theory. Furthermore, we find the analogous Kahler structure for the N=4 preserving Coulomb branch flows, and for an N=2 flow. In addition, we establish similar properties for two eleven dimensional flow geometries recently presented in the literature, one of which has a deformation of the conifold as its moduli space. In all of these cases, we notice that the Kahler potential appears to satisfy a simple universal differential equation. We prove that this equation arises for all purely Coulomb branch flows dual to both ten and eleven dimensional geometries, and conjecture that the equation holds much more generally.
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arxiv:hep-th/0107261
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Classical version of Born-Infeld electrodynamics is recalled and its most important properties discussed. Then we analyze possible abelian and non-abelian generalizations of this theory, and show how certain soliton-like configurations can be obtained. The relationship with the Standard Model of electroweak interactions is also mentioned.
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arxiv:hep-th/0108026
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Assuming the completeness condition for boundaries we derive trace formulas for the annulus coefficients in 2-dimensional conformal field theory. We also derive polynomial equations that relate the annulus, Moebius and Klein bottle coefficients, and conjecture an annulus trace formula that is sensitive to the orientation of the boundaries.
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arxiv:hep-th/0108035
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A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It facilitates both the construction of an appropriate infrared cutoff and the projection of the renormalization group flow onto a large class of truncated parameter spaces. The Einstein-Hilbert truncation is investigated in detail and the fixed point structure of the resulting flow is analyzed. Both a Gaussian and a non-Gaussian fixed point are found. If the non-Gaussian fixed point is present in the exact theory, quantum Einstein gravity is likely to be renormalizable at the nonperturbative level. In order to assess the reliability of the truncation a comprehensive analysis of the scheme dependence of universal quantities is performed. We find strong evidence supporting the hypothesis that 4-dimensional Einstein gravity is asymptotically safe, i.e. nonperturbatively renormalizable. The renormalization group improvement of the graviton propagator suggests a kind of dimensional reduction from 4 to 2 dimensions when spacetime is probed at sub-Planckian length scales.
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arxiv:hep-th/0108040
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In built noncommutativity of supermembranes with central charges in eleven dimensions is disclosed. This result is used to construct an action for a noncommutative supermembrane where interesting topological terms appear. In order to do so, we first set up a global formulation for noncommutative Yang Mills theory over general symplectic manifolds. We make the above constructions following a pure geometrical procedure using the concept of connections over Weyl algebra bundles on symplectic manifolds. The relation between noncommutative and ordinary supermembrane actions is discussed.
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arxiv:hep-th/0108046
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An alternative approach to introducing gravitational dynamics on a brane embedded in a higher dimensional spacetime is presented. The brane is treated as a boundary of a higher dimensional manifold in which the bulk action is described by a metric independent topological quantum field theory. The example of a five dimensional non-Abelian BF theory with a boundary brane is considered. A natural boundary condition is adopted chosen for consistency of the topological action despite the presence of a boundary. The resulting effective action on the brane is the action of general relativity in first order form plus terms involving the extrinsic curvature of the brane.
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arxiv:hep-th/0108066
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In this Letter we consider the problem of partial masslessness and unitarity in (A)dS using gauge invariant description of massive high spin particles. We show that for S = 2 and S = 3 cases such formalism allows one correctly reproduce all known results. Then we construct a gauge invariant formulation for massive particles of arbitrary integer spin s in arbitrary space-time dimension d. For d = 4 our results confirm the conjecture made recently by Deser and Waldron.
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arxiv:hep-th/0108192
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We consider the construction of fluxbranes in certain curved geometries, generalizing the familiar construction of the Melvin fluxtube as a quotient of flat space. The resulting configurations correspond to fluxbranes wrapped on cycles in curved spaces. The non-trivial transverse geometry leads in some instances to solutions with asymptotically constant dilaton profiles. We describe explicitly several supersymmetric solutions of this kind. The solutions inherit some properties from their flat space cousins, like flux periodicity. Interestingly type IIA/0A fluxbrane duality holds near the core of these fluxbranes, but does not persist in the asymptotic region, precisely where it would contradict perturbative inequivalence of IIA/0A theories.
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arxiv:hep-th/0108196
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We construct and check by explicit Feynman diagram calculations the BRST Ward identities for N=2 rigid super Yang-Mills theory and N=2 extended supergravity in four-dimensional Euclidean space without auxiliary fields. We use the Batalin-Vilkovisky formalism. In the supergravity case we need one new contractible pair of complex spinor fields to obtain the usual gauge-fixing term and corresponding Nielsen-Kallosh ghosts.
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arxiv:hep-th/0108204
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We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B. Zamolodchikov's (unpublished) formulae for the boundary energy and the relation between the Lagrangian (ultraviolet) and bootstrap (infrared) parameters. These results have been checked against numerical finite volume spectra coming from the truncated conformal space approach. We find an entirely consistent picture and strong evidence for the validity of the conjectured spectrum and scattering amplitudes, which together give a complete description of the boundary sine-Gordon theory on mass shell.
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arxiv:hep-th/0108211
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We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of SU(2) invariance of the noncommutative model.
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arxiv:hep-th/0108216
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This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.
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arxiv:hep-th/0108236
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In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum algebra operators is suggested by extending the definition of matrix elements of a physical observable, including the eventual projection on the appropriate symmetric space. This allows to build in the Lie space of representations one-parameter families of operators belonging to the enveloping Lie algebra that satisfy an approximate symmetry and have the properties required by physics.
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arxiv:hep-th/0109026
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We examine the low-energy dynamics of CP^1 lumps coupled to gravity, taking into account the gravitational back-reaction of the spacetime geometry. We show that the single lump moduli space is equipped with a three-dimensional metric, and we derive stability bounds on the scalar coupling constant. We also derive an expression for the multi-lump moduli space metric.
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arxiv:hep-th/0109123
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The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.
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arxiv:hep-th/0109153
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We consider the dynamical stability of a static brane model that incorporates a three-index antisymmetric tensor field and has recently been proposed as a possible solution to the cosmological constant problem. Ultimately, we are able to establish the existence of time-dependent, purely gravitational perturbations. As a consequence, the static solution of interest is ``dangerously'' located at an unstable saddle point. This outcome is suggestive of a hidden fine tuning in what is an otherwise self-tuning model.
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arxiv:hep-th/0109180
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We consider the ultra-violet divergence structure of general noncommutative supersymmetric $U(N_c)$ gauge theories, and seek theories which are all-orders finite.
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arxiv:hep-th/0109195
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Using the path-integral formalism, we generalize the 't Hooft-Veltman method of unitary regulators to put forward a framework for finite, alternative quantum theories to a given quantum field theory. Feynman-like rules of such a finite, alternative quantum theory lead to alternative, perturbative Green functions. Which are acceptably regularized perturbative expansions of the original Green functions, causal, and imply no unphysical free particles. To demonstrate that the proposed framework is feasible, we take the quantum field theory of a single, self-interacting real scalar field and show how we can alter, covariantly and locally, its free-field Lagrangian to obtain finite, alternative perturbative Green functions.
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arxiv:hep-th/0110010
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We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely classified by irreducible unitary representations of G. It is not necessary to assume that the action of G on M is either free or transitive. Hence the quotient space M/G may have orbifold singularities. Stratification geometry, which is a generalization of the concept of principal fiber bundle, is necessarily introduced to describe the path integral on M/G. Using it we show that the reduced path integral is expressed as a product of three factors; the rotational energy amplitude, the vibrational energy amplitude, and the holonomy factor.
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arxiv:hep-th/0110015
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We consider Yang-Mills theory in Euclidean space-time $(R^4)$ and construct its configuration space. The orbits are first shown to form a congruence set. Then we discuss the orthogonal gauge condition in Abelian theory and show that Coulomb-like surfaces foliate the entire configuration space. In the non-Abelian case, where these exists no global orthogonal gauge, we derive the non-linear gauge proposed previously by the author by modifying the orthogonality condition. However, unlike the Abelian case, the entire configuration space cannot be foliated by submanifolds defined by the non-linear gauge. The foliation is only limited to the non-perturbative regime of Yang-Mills theory.
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arxiv:hep-th/0110038
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We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of the boundary parameters, the Bethe Ansatz solution is formulated in terms of Jacobian elliptic functions.
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arxiv:hep-th/0110081
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We examine string field algebra which is generated by star product in Witten's string field theory including ghost part. We perform calculations using oscillator representation consistently. We construct wedge like states in ghost part and investigate algebras among them. As a by-product we have obtained some solutions of vacuum string field theory. We also discuss some problems about identity state. We hope these calculations will be useful for further investigation of Witten type string field theory.
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arxiv:hep-th/0110124
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We investigate fluxbrane solutions to the Einstein-antisymmetric form-dilaton theory in arbitrary space-time dimensions for a transverse space of cylindrical topology $S^k\times R^n$, corresponding to smeared and unsmeared solutions. A master equation for a single metric function is derived. This is a non-linear second-order ordinary differential equation admitting an analytic solution, singular at the origin, which serves as an attractor for globally regular solutions, whose existence is demonstrated numerically. For all fluxbranes of different levels of smearing the metric function diverges at infinity as the same power of the radial coordinate except for the maximally smeared case, where a global solution is known in closed form and can be obtained algebraically using U-duality. The particular cases of F6 and F3 fluxbranes in D=11 supergravity and fluxbranes in IIA, IIB supergravities are discussed.
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arxiv:hep-th/0110164
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We discuss the problems of dark matter, quantum gravity, and vacuum energy within the context of a theory for which Lorentz invariance is not postulated, but instead emerges as a natural consequence in the physical regimes where it has been tested.
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arxiv:hep-th/0110208
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We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying quantum field dynamics in the presence of external uniform magnetic field: here, the field transformation serves to separate the dynamics within the given Landau level from that between different Landau levels. We apply this formalism to both nonrelativistic and relativistic field theories. In the large external magnetic field our formalism provides an efficient method for constructing the relevant lower-dimensional effective field theories with the field degrees defined only on the lowest Landau level.
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arxiv:hep-th/0110249
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We find a description of hybrid inflation in (3+1)-dimensions using brane dynamics of Hanany-Witten type. P-term inflation/acceleration of the universe with the hybrid potential has a slow-roll de Sitter stage and a waterfall stage which leads towards an N=2 supersymmetric ground state. We identify the slow-roll stage of inflation with a non-supersymmetric `Coulomb phase' with Fayet-Iliopoulos term. This stage ends when the mass squared of one of the scalars in the hypermultiplet becomes negative. At that moment the brane system starts undergoing a phase transition via tachyon condensation to a fully Higgsed supersymmetric vacuum which is the absolute ground state of P-term inflation. A string theory/cosmology dictionary is provided, which leads to constraints on parameters of the brane construction from cosmological experiments. We display a splitting of mass levels reminiscent of the Zeeman effect due to spontaneous supersymmetry breaking.
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arxiv:hep-th/0110271
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The problem of the restoring of the equivalence between Light-Front (LF) Hamiltonian and conventional Lorentz-covariant formulations of gauge theory is solved for QED(1+1) and (perturbatively to all orders) for QCD(3+1). For QED(1+1) the LF Hamiltonian is constructed which reproduces the results of Lorentz-covariant theory. This is achieved by bosonization of the model and by analysing the resulting bosonic theory to all orders in the fermion mass. For QCD(3+1) we describe nonstandard regularization that allows to restore mentioned equivalence with finite number of counterterms in LF Hamiltonian.
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arxiv:hep-th/0111009
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We investigate the modular transformation properties of observable (light) fields in heterotic orbifolds, in the light of recent calculations of CP-violating quantities. Measurable quantities must be modular invariant functions of string moduli, even if the light fields are noninvariant. We show that physical invariance may arise by patching smooth functions that are separately noninvariant. CP violation for <T> on the unit circle, which requires light and heavy states to mix under transformation, is allowed in principle, although the Jarlskog parameter J_CP(T) must be amended relative to previous results. However, a toy model of modular invariant mass terms indicates that the assumption underlying these results is unrealistic. In general the mass eigenstate basis is manifestly modular invariant and coupling constants are smooth invariant functions of T, thus CP is unbroken on the unit circle. We also discuss the status of CP-odd quantities when CP is a discrete gauge symmetry, and point out a link with baryogenesis.
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arxiv:hep-th/0111024
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The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived using the ``exotic'' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.
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arxiv:hep-th/0111033
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A role of the renormalization group invariance in calculations of the ground state energy for models with confined fermion fields is discussed. The case of the (1+1)D MIT bag with massive fermions is studied in detail.
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arxiv:hep-th/0111037
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We establish a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces. M-theory on T^k corresponds to P^2 blown up at k generic points; Type IIB corresponds to P^1\times P^1. The moduli of compactifications of M-theory on rectangular tori are mapped to Kahler moduli of del Pezzo surfaces.The U-duality group of M-theory corresponds to a group of classical symmetries of the del Pezzo represented by global diffeomorphisms. The half-BPS brane charges of M-theory correspond to spheres in the del Pezzo, and their tension to the exponentiated volume of the corresponding spheres. The electric/magnetic pairing of branes is determined by the condition that the union of the corresponding spheres represent the anticanonical class of the del Pezzo. The condition that a pair of half-BPS states form a bound state is mapped to a condition on the intersection of the corresponding spheres. We present some speculations about the meaning of this duality.
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arxiv:hep-th/0111068
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We argue that the worldvolume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit `deconstruction' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite `fuzzy moose' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.
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arxiv:hep-th/0111079
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We study the star algebra of ghost sector in vacuum string field theory (VSFT). We show that the star product of two states in the Siegel gauge is BRST exact if we take the BRST charge to be the one found in hep-th/0108150, and the BRST exact states are nil factors in the star algebra. By introducing a new star product defined on the states in the Siegel gauge, the equation of motion of VSFT is characterized as the projection condition with respect to this new product. We also comment on the comma form of string vertex in the ghost sector.
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arxiv:hep-th/0111087
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We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone. Applications to a variety of D-brane geometries are described in some detail.
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arxiv:hep-th/0111113
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Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra C_2 is obtained. The functions H_1 and H_2 for this solution are polynomials of degree 3 and 4.
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arxiv:hep-th/0111219
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In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two ($1 + 1$)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four ($2 + 2)$-dimensional supermanifold.
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arxiv:hep-th/0111253
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We investigate the charged Schwarzschild-Anti-deSitter (SAdS) BH thermodynamics in 5d Einstein-Gauss-Bonnet gravity with electromagnetic field. The Hawking-Page phase transitions between SAdS BH and pure AdS space are studied. The corresponding phase diagrams (with critical line defined by GB term coefficient and electric charge) are drawn. The possibility to account for higher derivative Maxwell terms is mentioned. In frames of proposed dS/CFT correspondence it is demonstrated that brane gravity maybe localized similarly to AdS/CFT. SdS BH thermodynamics in 5d Einstein and Einstein-Gauss-Bonnet gravity is considered. The corresponding (complicated) surface counterterms are found and used to get the conserved BH mass, free energy and entropy. The interesting feature of of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. We speculate that the appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur.
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arxiv:hep-th/0112045
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The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation, it gives out classical Newton's theory of gravity. It can also give out Einstein's field equation with cosmological constant. For classical tests, it gives out the same theoretical predictions as those of general relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.
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arxiv:hep-th/0112062
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Seven-manifolds of G_2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G_2 metrics D_7, with S^3\times S^3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B_7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D_7 metrics' non-trivial parameter characterises the squashing of an S^3 bolt, which limits to S^2 at weak coupling. In general the D_7 metrics are asymptotically locally conical, with a nowhere-singular circle action.
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arxiv:hep-th/0112098
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The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this procedure. On the other hand, it is convenient to reorganize the constraints such that they are explicitly decomposed into the first-class and second-class constraints. We discuss the reorganization of the constraints into the first- and second-class constraints that is consistent with the Dirac procedure, i.e., that does not violate the decomposition of the constraints according to the stages of the Dirac procedure. The possibility of such a reorganization is important for the study of gauge symmetries in the Lagrangian and Hamiltonian formulations.
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arxiv:hep-th/0112103
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A supersymmetric formulation of a three-dimensional SYM-Chern-Simons theory using light-cone quantization is presented, and the supercharges are calculated in light-cone gauge. The theory is dimensionally reduced by requiring all fields to be independent of the transverse dimension. The result is a non-trivial two-dimensional supersymmetric theory with an adjoint scalar and an adjoint fermion. We perform a numerical simulation of this SYM-Chern-Simons theory in 1+1 dimensions using SDLCQ (Supersymmetric Discrete Light-Cone Quantization). We find that the character of the bound states of this theory is very different from previously considered two-dimensional supersymmetric gauge theories. The low-energy bound states of this theory are very ``QCD-like.'' The wave functions of some of the low mass states have a striking valence structure. We present the valence and sea parton structure functions of these states. In addition, we identify BPS-like states which are almost independent of the coupling. Their masses are proportional to their parton number in the large-coupling limit.
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arxiv:hep-th/0112151
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The character of the principal series of representations of SL(n,R) is evaluated by using Gel'fand and Naimark's definition of character. This representation is realized in the space of functions defined on the right coset space of SL(n,R) with respect to the subgroup of real triangular matrices. This form of the representations considerably simplifies the problem of determination of the integral kernel of the group ring which is fundamental in the Gel'fand-Naimark theory of character. An important feature of the principal series of representations is that the `elliptic' elements of SL(n,R) do not contribute to its character.
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arxiv:hep-th/0112245
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We clarify RR tadpole cancellation conditions for intersecting D4-/D5-branes. We find all of the D4-brane models which have D=4 three-generation chiral fermions with the SU(3)XSU(2)XU(1)^n symmetries. For the D5-brane case, we present a solution to the conditions which gives exactly the matter contents of standard model with U(1) anomalies.
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arxiv:hep-th/0112247
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Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional structures specific to eleven dimensions leads us to exceptional groups in the description of space-time. One specific connection, through the coset $F_4/SO(9)$, may provide a generalization of eleven-dimensional supergravity. Since this coset happens to be the projective space of the Exceptional Jordan Algebra, its charge space may be linked to the fundamental degrees of freedom underlying M-theory.
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arxiv:hep-th/0112261
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We compute the three-graviton tree amplitude in Type IIB superstring theory compactified to six dimensions using the manifestly (6d) supersymmetric Berkovits-Vafa-Witten worldsheet variables. We consider two cases of background geometry: the flat space example R6xK3, and the curved example AdS3xS3xK3 with Ramond flux, and compute the correlation functions in the bulk.
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arxiv:hep-th/0201027
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According to the holography principle (due to G.`t Hooft, L. Susskind, J. Maldacena, et al.), quantum gravity and string theory on certain manifolds with boundary can be studied in terms of a conformal field theory on the boundary. Only a few mathematically exact results corroborating this exciting program are known. In this paper we interpret from this perspective several constructions which arose initially in the arithmetic geometry of algebraic curves. We show that the relation between hyperbolic geometry and Arakelov geometry at arithmetic infinity involves exactly the same geometric data as the Euclidean AdS_3 holography of black holes. Moreover, in the case of Euclidean AdS_2 holography, we present some results on bulk/boundary correspondence where the boundary is a non-commutative space.
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arxiv:hep-th/0201036
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This short note was born out of discussions on anyons in the FQHE at the YITP workshop "Fundamental problems of quantum field theories" (December 19-21, 2001, YITP, Kyoto). At that time, I felt that there might not be a sound consensus of opinion on the subject. Now, I would like to show my understanding here, the essential part of which is based on hep-th/0110197. The first problem discussed is a notion of ``bosonized electrons (bosonization)", which are unphysical objects from the standpoint of the Chern-Simons gauge invariance. Therefore, their condensate is merely of mathematical concept and the true physical state realized is a liquid-like one made of degeneration of anyons. Based on this recognition, I argue about a mechanism of the degeneration that results from the genuine CS gauge field theory. It is noted that the Ginzburg-Landau effective theory is not necessary. As the last problem, the gauge invariance in the "composite-fermion theories" is discussed.
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arxiv:hep-th/0201053
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We review the procedure by which we implemented the non-Abelian Gauss's law and constructed gauge-invariant fields for QCD in the temporal (Weyl) gauge. We point out that the operator-valued transformation that transforms gauge-dependent temporal-gauge fields into gauge-invariant ones has the formal structure of a gauge transformation. We express the ``standard'' Hamiltonian for temporal-gauge QCD entirely in terms of gauge-invariant fields, calculate the commutation rules for these fields, and compare them to earlier work on Coulomb-gauge QCD. We also discuss multiplicities of gauge-invariant temporal-gauge fields that belong to different topological sectors and that, in previous work, were shown to be based on the same underlying gauge-dependent temporal-gauge fields. We relate these multiplicities of gauge-invariant fields to Gribov copies. We argue that Gribov copies appear in the temporal gauge, but not when the theory is represented in terms of gauge-dependent fields and Gauss's law is left unimplemented. There are Gribov copies of the gauge-invariant gauge field, which can be constructed when Gauss's law is implemented.
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arxiv:hep-th/0201069
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It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the Kodaira-Spencer deformation theory of complex structures are discussed. Subsequently, some field theoretical aspects at the classical level are briefly underlined.
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arxiv:hep-th/0201071
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Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analytically and a limited set of eigenfunctions is constructed explicitly.
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arxiv:hep-th/0201080
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We show by some counterexamples that Lagrangian sysytems with nonlocality of finite extent are not necessarily unstable.
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arxiv:hep-th/0201087
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The formulation of Seiberg-Witten maps from the point of view of consistent deformations of gauge theories in the context of the Batalin-Vilkovisky antifield formalism is reviewed. Some additional remarks on noncommutative Yang-Mills theory are made.
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arxiv:hep-th/0201139
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The Lie algebra of Feynman graphs gives rise to two natural representations, acting as derivations on the commutative Hopf algebra of Feynman graphs, by creating or eliminating subgraphs. Insertions and eliminations do not commute, but rather establish a larger Lie algebra of derivations which we here determine.
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arxiv:hep-th/0201157
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Taking seriously the hypothesis that the full symmetry algebra of M-theory is osp(1|32,R), we derive the supersymmetry transformations for all fields that appear in 11- and 12-dimensional realizations and give the associated SUSY algebras. We study the background-independent osp(1|32,R) cubic matrix model action expressed in terms of representations of the Lorentz groups SO(10,2) and SO(10,1). We explore further the 11-dimensional case and compute an effective action for the BFSS-like degrees of freedom. We find the usual BFSS action with additional terms incorporating couplings to transverse 5-branes, as well as a mass-term and an infinite tower of higher-order interactions.
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arxiv:hep-th/0201183
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We present a class of chiral non-supersymmetric D=4 field theories in which quadratic divergences appear only at two loops. They may be depicted as ``SUSY quivers'' in which the nodes represent a gauge group with extended e.g., N=4 SUSY whereas links represent bifundamental matter fields which transform as chiral multiplets with respect to different N=1 subgroups. One can obtain this type of field theories from simple D6-brane configurations on Type IIA string theory compactified on a six-torus. We discuss the conditions under which this kind of structure is obtained from D6-brane intersections. We also discuss some aspects of the effective low-energy field theory. In particular we compute gauge couplings and Fayet-Iliopoulos terms from the Born-Infeld action and show how they match the field theory results. This class of theories may be of phenomenological interest in order to understand the modest hierarchy problem i.e., the stability of the hierarchy between the weak scale and a fundamental scale of order 10-100 TeV which appears e.g. in low string scale models. Specific D-brane models with the spectrum of the SUSY Standard Model and three generations are presented.
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arxiv:hep-th/0201205
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The relationship between Elliptic Ruijsenaars-Schneider (RS) and Calogero-Moser (CM) models with Sklyanin algebra is presented. Lax pair representations of the Elliptic RS and CM are reviewed. For n=2 case, the eigenvalue and eigenfunction for Lame equation are found by using the result of the Bethe ansatz method.
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arxiv:hep-th/0201211
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We describe generalized D=11 Poincar\'{e} and conformal supersymmetries. The corresponding generalization of twistor and supertwistor framework is outlined with $OSp(1|64)$ superspinors describing BPS preons. The $\frac{k}{32}$ BPS states as composed out of $n=32 - k$ preons are introduced, and basic ideas concerning BPS preon dynamics is presented. The lecture is based on results obtained by J.A. de Azcarraga, I. Bandos, J.M. Izquierdo and the author$^1$.
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arxiv:hep-th/0201233
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A proposal towards a microscopic understanding of the Bekenstein-Hawking entropy for D=4 spacetimes with event horizon is made. Since we will not rely on supersymmetry these spacetimes need not be supersymmetric. Euclidean D-branes which wrap the event horizon's boundary will play an important role. After arguing for a discretization of the Euclidean D-brane worldvolume based on the worldvolume uncertainty relation, we count chainlike excitations on the worldvolume of specific dual Euclidean brane pairs. Without the need for supersymmetry it is shown that one can thus reproduce the D=4 Bekenstein-Hawking entropy and its logarithmic correction.
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arxiv:hep-th/0201260
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We obtain an analytic approximation for the effective action of a quantum scalar field in a general static two-dimensional spacetime. We apply this to the dilaton gravity model resulting from the spherical reduction of a massive, non-minimally coupled scalar field in the four-dimensional Schwarzschild geometry. Careful analysis near the event horizon shows the resulting two-dimensional system to be regular in the Hartle-Hawking state for general values of the field mass, coupling, and angular momentum, while at spatial infinity it reduces to a thermal gas at the black-hole temperature.
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arxiv:hep-th/0202036
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If our 3+1-dimensional universe is a brane or domain wall embedded in a higher dimensional space, then a phenomenon we term the ``clash of symmetries'' provides a new method of breaking some continuous symmetries. A global $G_{\text{cts}} \otimes G_{\text{discrete}}$ symmetry is spontaneously broken to $H_{\text{cts}} \otimes H_{\text{discrete}}$, where the continuous subgroup $H_{\text{cts}}$ can be embedded in several different ways in the parent group $G_{\text{cts}}$, and $H_{\text{discrete}} < G_{\text{discrete}}$. A certain class of topological domain wall solutions connect two vacua that are invariant under {\it differently embedded} $H_{\text{cts}}$ subgroups. There is then enhanced symmetry breakdown to the intersection of these two subgroups on the domain wall. This is the ``clash''. In the brane limit, we obtain a configuration with $H_{\text{cts}}$ symmetries in the bulk but the smaller intersection symmetry on the brane itself. We illustrate this idea using a permutation symmetric three-Higgs-triplet toy model exploiting the distinct $I-$, $U-$ and $V-$spin U(2) subgroups of U(3). The three disconnected portions of the vacuum manifold can be treated symmetrically through the construction of a three-fold planar domain wall junction configuration, with our universe at the nexus. A possible connection with $E_6$ is discussed.
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arxiv:hep-th/0202042
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It is shown that the Holographic Renormalization Group can be formulated universally within Quantum Field Theory as (the quantization of) the Hamiltonian flow on the cotangent bundle to the space of gauge-invariant single-trace operators supplied with the canonical symplectic structure. The classical Hamiltonian dynamics is recovered in the large $N$ limit.
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arxiv:hep-th/0202055
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We consider the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO_{(\pm)}(d)$ Yang--Mills hierarchy, in $d$ dimensions. Such systems can occur in the low energy effective action of string theory. Particle-like solutions %for the systems with only an Einstein term, and with only a GB term, in dimensions $d=6,8$ are constructed respectively. Our results reveal qualitatively new properties featuring double-valued solutions with critical behaviour. In this preliminary study, we have restricted ourselves to one-node solutions.
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arxiv:hep-th/0202141
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We probe the U(N) chiral Gross-Neveu model with a source-term $J\l{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter $d$. We obtain a non-perturbative mass gap as the solution of $\hat{J}=0$. A physical choice for $d$ gives good results for $N>2$. The self-consistent minimal sensitivity condition gives a slight improvement.
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arxiv:hep-th/0202194
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A proposal is made for a cosmological D3/D7 model with a constant magnetic flux along the D7 world-volume. It describes an N=2 gauge model with Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The motion of the D3-brane towards D7 in a phase with spontaneously broken supersymmetry provides a period of slow-roll inflation in the de Sitter valley, the role of the inflaton being played by the distance between D3 and D7-branes. After tachyon condensation a supersymmetric ground state is formed: a D3/D7 bound state corresponding to an Abelian non-linear (non-commutative) instanton. In this model the existence of a non-vanishing cosmological constant is associated with the resolution of the instanton singularity. We discuss a possible embedding of this model into a compactified M-theory setup.
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arxiv:hep-th/0203019
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First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of the stratification and the natural Riemannian structures of the strata. In the second part, we study the stratification for theories with gauge group $\rmSU(n)$ in space time dimension 4. We develop a general method for determining the orbit types and their partial ordering, based on the 1-1 correspondence between orbit types and holonomy-induced Howe subbundles of the underlying principal $\rmSU(n)$-bundle. We show that the orbit types are classified by certain cohomology elements of space time satisfying two relations and that the partial ordering is characterized by a system of algebraic equations. Moreover, operations for generating direct successors and direct predecessors are formulated, which allow one to construct the set of orbit types, starting from the principal one. Finally, we discuss an application to nodal configurations in topological Chern-Simons theory.
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arxiv:hep-th/0203027
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We construct some classes of instanton solutions of eight dimensional noncommutative ADHM equations generalizing the solutions of eight dimensional commutative ADHM equations found by Papadopoulos and Teschendorff, and interpret them as supersymmetric $D0$-$D8$ bound states in a NS $B$-field. Especially, we consider the $D0$-$D8$ system with anti-self-dual $B$-field preserving 3/16 of supercharges. This system and self-duality conditions are related with the group $Sp(2)$ which is a subgroup of the eight dimensional rotation group SO(8).
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arxiv:hep-th/0203047
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In this Report we review the microscopic formulation of the five dimensional black hole of type IIB string theory in terms of the D1-D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1-D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.
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arxiv:hep-th/0203048
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In this work we review some features of topological defects in field theory models for real scalar fields. We investigate topological defects in models involving one and two or more real scalar fields. In models involving a single field we examine two different subclasses of models, which support one or more topological defects. In models involving two or more real scalar fields, we explore the presence of defects that live inside topological defects, and junctions and networks of defects. In the case of junctions of defects we investigte structures that simulate nanotubes and fulerenes. Our investigations may also be used to describe nonlinear properties of polymers, Langmuir films and optical solitons in fibers.
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arxiv:hep-th/0203050
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The physical world is marked by the phenomenon of spontaneous broken symmetry (SBS) i.e. where the state of a system is assymmetric with respect to the symmetry principles that govern its dynamics. For material systems this is not surprising since more often than not energetic considerations dictate that the ground state or low lying excited states of many body system become ordered i.e. a collective variable, such as magnetization or the Fourier transform of the density of a solid, picks up expectation values which otherwise would vanish by virtue of the dynamical symmetry(isotropy or translational symmetry in the aforementioned examples). More surprising was the discovery of the role of SBS in describing the vacuum or low lyng excitations of a quantum field theory. First came spontaneously broken chiral symmetry which was then applied to soft pion physics. When combined with current algebra, this field dominated particle physics in the 60's. Then came the application of the notion of SBS to situations where the symmetry is locally implemented by gauge fields. In that case the concept of order becomes more subtle. This development lead the way to electroweak unification and it remains one of the principal tools of the theorist in the quest for physics beyond the standard model. This brief review is intended to span the history of SBS with emphasis on conceptual rather than quantitative content. It is a written version of lectures of R.Brout on the ``Paleolithic Age'' and on ``Modern Times'' by F.Englert, i.e. respectively without and with gauge fields.
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arxiv:hep-th/0203096
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We propose a variation of spacetime noncommutative field theory to realize the stringy spacetime uncertainty relation without breaking any of the global symmetries of the homogeneous isotropic universe. We study the spectrum of metric perturbations in this model for a wide class of accelerating background cosmologies. Spacetime noncommutativity leads to a coupling between the fluctuation modes and the background cosmology which is nonlocal in time. For each mode, there is a critical time at which the spacetime uncertainty relation is saturated. This is the time when the mode is generated. These effects lead to a spectrum of fluctuations whose spectral index is different from what is obtained for commutative spacetime in the infrared region, but is unchanged in the ultraviolet region. In the special case of an exponentially expanding background, we find a scale-invariant spectrum. but with a different magnitude than in the context of commutative spacetime if the Hubble constant is above the string scale.
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arxiv:hep-th/0203119
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Starting from the Maldacena-Nunez supergravity dual of N=1 super Yang-Mills theory we study the inclusion of a supersymmetry breaking gaugino mass term. We consider a class of non supersymmetric deformations of the MN solutions which have been recently proposed in the literature. We show that they can be interpreted as corresponding to the inclusion of both a mass and a condensate. We calculate the vacuum energy of the supergravity solutions showing that the N-fold vacuum degeneracy of the N=1 theory is lifted by the inclusion of a mass term.
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arxiv:hep-th/0203203
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We examine the conjecture that an 11d E_8 bundle, appearing in the calculation of phases in the M-Theory partition function, plays a physical role in M-Theory, focusing on consequences for the classification of string theory solitons. This leads for example to a classification of IIA solitons in terms of that of LE_8 bundles in 10d. Since K(Z,2) approximates LE_8 up to \pi_{14}, this reproduces the K-Theoretic classification of IIA D-branes while treating NSNS and RR solitons more symmetrically and providing a natural interpretation of G_0 as the central extension of LE_8.
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arxiv:hep-th/0203218
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We consider open strings ending on a D5-brane in the pp-wave background, which is realized in the Penrose limit of $AdS_5 \times S^5$ with an $AdS_4\times S^2$ brane. A complete list of gauge invariant operators in the defect conformal field theory is constructed which is dual to the open string states.
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arxiv:hep-th/0203257
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A class of black objects which are solutions of pure gravity with negative cosmological constant are classified through the mapping between the Killing spinors of the ground state and those of the transverse section. It is shown that these geometries must have transverse sections of constant curvature for spacetime dimensions d below seven. For d > 6, the transverse sections can also be Euclidean Einstein manifolds. In even dimensions, spacetimes with transverse section of nonconstant curvature exist only in d = 8 and 10. This classification goes beyond standard supergravity and the eleven dimensional case is analyzed. It is shown that if the transverse section has negative scalar curvature, only extended objects can have a supersymmetric ground state. In that case, some solutions are explicitly found whose ground state resembles a wormhole.
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arxiv:hep-th/0204029
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We study cosmology on a BPS D3-brane evolving in the 10D SUGRA background describing a non-BPS brane. Initially the BPS brane is taken to be a probe whose dynamics we determine in the non-compact non-BPS background. The cosmology observed on the brane is of the FRW type with a scale factor $S(\tau)$. In this mirage cosmology approach, there is no self-gravity on the brane which cannot inflate. Self-gravity is then included by compactifying the background space-time. The low energy effective theory below the compactification scale is shown to be bi-metric, with matter coupling to a different metric than the geometrically induced metric on the brane. The geometrical scale factor on the brane is now $S(\tau) a(\tau)$ where $a(\tau)$ arises from brane self-gravity. In this non-BPS scenario the brane generically inflates. We study the resulting inflationary scenario taking into account the fact that the non-BPS brane eventually decays on a time-scale much larger than the typical inflationary time-scale. After the decay, the theory ceases to be bi-metric and COBE normalization is used to estimate the string scale which is found to be of order $10^{14}$ GeV.
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arxiv:hep-th/0204120
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We consider self tuning solutions for a brane embedded in an anti de Sitter spacetime. We include the higher derivative Gauss-Bonnet terms in the action and study singularity free solutions with finite effective Newton's constant. Using the methods of Csaki et al, we prove that such solutions, when exist, always require a fine tuning among the brane parameters. We then present a new method of analysis in which the qualitative features of the solutions can be seen easily without obtaining the solutions explicitly. Also, the origin of the fine tuning is transparent in this method.
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arxiv:hep-th/0204136
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We describe two extensions of the notion of a self-dual connection in a vector bundle over a manifold M from dim M=4 to higher dimensions. The first extension, Omega-self-duality, is based on the existence of an appropriate 4-form Omega on the Riemannian manifold M and yields solutions of the Yang-Mills equations. The second is the notion of half-flatness, which is defined for manifolds with certain Grassmann structure T^C M \cong E \otimes H. In some cases, for example for hyper-Kaehler manifolds M, half-flatness implies Omega-self-duality. A construction of half-flat connections inspired by the harmonic space approach is described. Locally, any such connection can be obtained from a free prepotential by solving a system of linear first order ODEs.
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arxiv:hep-th/0205030
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We discuss the correspondence point between a string state and a black hole, in a pp-wave background, and find that the answer is considerably different from that in a flat spacetime background.
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arxiv:hep-th/0205043
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Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on $\kappa$-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally constructed by introducing a suitable generating functional for Green functions in energy-momentum space. Direct reference to a star product is not necessary. It is sufficient to make use of the simple properties that the Fourier transform preserves in these spacetimes and establish the rules for products of wave exponentials that are dictated by the non-commutativity of the coordinates. The approach also provides an elementary description of "planar" and "non-planar" Feynman diagrams. We also comment on the rich phenomenology emerging from the analysis of these theories.
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arxiv:hep-th/0205047
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Paper withdrawn due to a crucial algebraic error in section 3.
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arxiv:hep-th/0205049
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We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.
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arxiv:hep-th/0205083
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We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge and found that it is an integer, independent of the noncommutative parameters $\theta_{1,2}$.
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arxiv:hep-th/0205110
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We present a class of orthogonal membrane configurations which preserve 1/4 of the full type IIA supersymmetry. These membrane configurations carry additional F-string charges. We further analyze the D1-D3 configuration after applying T- duality along the world volume directions of the above orthogonal membranes.
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arxiv:hep-th/0205138
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We consider the tensor theory on coincident E8 5-branes compactified on a three torus. Using string theory, we predict that there must be distinct components in the moduli space of this theory.We argue that new superconformal field theories are to be found in these sectors with, for example, global G2 and F4 symmetries. In some cases, twisted E8 5-branes can be identified with small instantons in non-simply-laced gauge groups. This allows us to determine the Higgs branch for the fixed point theory. We determine the Coulomb branch by using an M theory dual description involving partially frozen singularities. Along the way, we show that a D0-brane binds to two D4-branes, but not to an Sp-type O4-plane (despite the existence of a Higgs branch). These results are used to check various string/string dualities for which, in one case (quadruple versus NVS), we present a new argument. Finally, we describe the construction of new non-BPS branes as domain walls in various heterotic/type I string theories.
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arxiv:hep-th/0205162
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This is a set of lectures on the gauge/string duality and non-critical strings, with a particular emphasis on the discretized, or matrix model, approach. After a general discussion of various points of view, I describe the recent generalization to four dimensional non-critical (or five dimensional critical) string theories of the matrix model approach. This yields a fully non-perturbative and explicit definition of string theories with eight (or more) supercharges that are related to four dimensional CFTs and their relevant deformations. The space-time as well as world-sheet dimensions of the supersymmetry preserving world-sheet couplings are obtained. Exact formulas for the central charge of the space-time supersymmetry algebra as a function of these couplings are calculated. They include infinite series of string perturbative contributions as well as all the non-perturbative effects. An important insight on the gauge theory side is that instantons yield a non-trivial 1/N expansion at strong coupling, and generate open string contributions, in addition to the familiar closed strings from Feynman diagrams. We indicate various open problems and future directions of research.
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arxiv:hep-th/0205171
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Gauge symmetry breaking through the Hosotani mechanism (the dynamics of nonintegrable phases) in softly broken supersymmetric QCD with $N_F^{fd}$ flavors is studied. For $N=$ even, there is a single SU(N) symmetric vacuum state, while for $N=$ odd, there is a doubly degenerate SU(N) symmetric vacuum state in the model. We also study generalized supersymmetric QCD by adding $N_F^{adj}$ numbers of massless adjoint matter. The gauge symmetry breaking pattern such as $SU(3)\to SU(2)\times U(1)$ is possible for appropriate choices of the matter content and values of the supersymmetry breaking parameter. The massless state of the adjoint Higgs scalar is also discussed in the models.
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arxiv:hep-th/0205173
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For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic oscillators calculated at the zero angular momentum. This type of an approximate Hermitization is valid in all the domain where the spectrum of energies remains real. It proves very efficient numerically. The construction is asymmetric with respect to the sign of the subdominant square-root spike, and exhibits a discontinuity at the point where the PT symmetric regularization vanishes.
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arxiv:hep-th/0205181
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We present the formalism of q-stars with local or global U(1) symmetry. The equations we formulate are solved numerically and provide the main features of the soliton star. We study its behavior when the symmetry is local in contrast to the global case. A general result is that the soliton remains stable and does not decay into free particles and the electrostatic repulsion preserves it from gravitational collapse. We also investigate the case of a q-star with non-minimal energy-momentum tensor and find that the soliton is stable even in some cases of collapse when the coupling to gravity is absent.
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arxiv:hep-th/0205197
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We study the superstring theory on pp-wave background with NSNS-flux that is realized as the Penrose limit of AdS_3 x S^3 x M^4, where M^4 is T^4 or T^4/Z_2(~ K3). Quantizing this system in the covariant gauge, we explicitly construct the space-time supersymmetry algebra and the complete set of DDF operators. We analyse the spectrum of physical states by using the spectrally flowed representations of current algebra. This spectrum is classified by the ``short string sectors'' and the ``long string sectors'' as in AdS_3 string theory. The states of the latter propagate freely along the transverse plane of pp-wave background, but the states of the former do not. We compare the short string spectrum with the BPS and almost BPS states which have large R-charges in the symmetric orbifold conformal theory, which is known as the candidate of dual theory of superstrings on AdS_3 x S^3 x M^4. We show that every short string states can be embedded successfully in the single particle Hilbert space of symmetric orbifold conformal theory.
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arxiv:hep-th/0205200
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Coupling fundamental quarks to QCD in the dual string representation corresponds to adding the open string sector. Flavors therefore should be represented by space-time filling D-branes in the dual 5d closed string background. This requires several interesting properties of D-branes in AdS. D-branes have to be able to end in thin air in order to account for massive quarks, which only live in the UV region. They must come in distinct sets, representing the chiral global symmetry, with a bifundamental field playing the role of the chiral condensate. We show that these expectations are born out in several supersymmetric examples. To analyze most of these properties it is not necessary to go beyond the probe limit in which one neglects the backreaction of the flavor D-branes.
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arxiv:hep-th/0205236
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There has been substantial interest in obtaining a quantum-gravitational description of de Sitter space. However, any such attempts have encountered formidable obstacles, and new philosophical directions may be in order. One possibility, although somewhat speculative, would be to view the physical universe as a timelike hypersurface evolving in a higher-dimensional bulk spacetime; that is, the renowned brane-world scenario. In this paper, we extend some recent studies along this line, and consider a non-critical 3-brane moving in the background of an anti-de Sitter Reissner-Nordstrom-like black hole. Interestingly, even an arbitrarily small electrostatic charge in the bulk can induce a singularity-free ``bounce'' universe on the brane, whereas a vanishing charge typically implies a singular cosmology. However, under closer examination, from a holographic (dS/CFT) perspective, we demonstrate that the charge-induced bounce cosmologies are not physically viable. This implies the necessity for censoring against charge in a bulk black hole.
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arxiv:hep-th/0205251
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We discuss the associativity or WDVV equations and demonstrate that they can be rewritten as certain functional relations between the {\it second} derivatives of a single function, similar to the dispersionless Hirota equations. The properties of these functional relations are further discussed.
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arxiv:hep-th/0205308
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The most popular noncommutative field theories are characterized by a matrix parameter theta^(mu,nu) that violates Lorentz invariance. We consider the simplest algebra in which the theta-parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology.
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arxiv:hep-th/0206035
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The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le 1$. For $\epsilon =1$ one recovers the covariance of a massless scalar field in $R^3$. For $\epsilon =0$ $\phi^{4}$ is a marginal interaction. For $0\le \epsilon < 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $\epsilon > 0$, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. These iterations converge to the fixed point on its stable (critical) manifold which is constructed.
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arxiv:hep-th/0206040
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In an attempt to bridge the gap between M-theory and braneworld phenomenology, we present various gravitational Lorentz-violating braneworlds which arise from p-brane systems. Lorentz invariance is still preserved locally on the braneworld. For certain p-brane intersections, the massless graviton is quasi-localized. This also results from an M5-brane in a C-field. In the case of a p-brane perturbed from extremality, the quasi-localized graviton is massive. For a braneworld arising from global AdS_5, gravitons travel faster when further in the bulk, thereby apparently traversing distances faster than light.
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arxiv:hep-th/0206050
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