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After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no {\it explicit} gravitational dressing factor, analogue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the gravitationally dressed four-point correlation function of products of left and right fermions. We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the power-law singularity in the absence of gravity. This rather surprising effect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansions. We also discuss some perturbative evidence that the chiral Gross-Neveu model may remain integrable when coupled to gravity.
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arxiv:hep-th/9503209
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For all Poincar\'e invariant Lagrangians of the form ${\cal L}\equiv f(F_{\mu\nu})$, in three Euclidean dimensions, where $f$ is any invariant function of a non-compact $U(1)$ field strength $F_{\mu\nu}$, we find that the only continuum limit (described by just such a gauge field) is that of free field theory: First we approximate a gauge invariant version of Wilson's renormalization group by neglecting all higher derivative terms $\sim \partial^nF$ in ${\cal L}$, but allowing for a general non-vanishing anomalous dimension. Then we prove analytically that the resulting flow equation has only one acceptable fixed point: the Gaussian fixed point. The possible relevance to high-$T_c$ superconductivity is briefly discussed.
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arxiv:hep-th/9503225
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We prove that particle models whose action is given by the integrated $n$-th curvature function over the world line possess $n+1$ gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by rephrasing the $n$-th curvature model in $\reals^d$ in terms of a standard relativistic particle in $S^{d-n}$. We ``prove by example'' that the algebra of these infinitesimal gauge invariances is nothing but $\W_{n+2}$, thus providing a geometrical picture of the $\W$-symmetry for these models. As a spin-off of our approach we give a new global invariant for four-dimensional curves subject to a curvature constraint.
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arxiv:hep-th/9504071
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We review the closed time path formalism of Schwinger using a path integral approach. We apply this formalism to the study of pair production from strong external fields as well as the time evolution of a nonequilibrium chiral phase transition.
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arxiv:hep-th/9504073
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Sufficiently large seeds for generating the observed (inter)galactic magnetic fields emerge naturally in string cosmology from the amplification of electromagnetic vacuum fluctuations due to a dynamical dilaton background. The success of the mechanism depends crucially on two features of the so-called pre-big-bang scenario, an early epoch of dilaton-driven inflation at very small coupling, and a sufficiently long intermediate stringy era preceding the standard radiation-dominated evolution.
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arxiv:hep-th/9504083
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We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy solutions (the sphalerons) which have been found earlier are rewritten in handy physical variables with the gauge condition $A_0 = 0$. Stationary solutions to the equations of motion in the Minkowski space-time (the standing waves) are discussed. We briefly discuss also the theory defined in a flat finite spherical box with rigid boundary conditions and present the numerical solution describing the sphaleron.
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arxiv:hep-th/9504117
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We study the topologically twisted osp(2|2)+osp(2|2) conformal superalgebra. The algebra includes the Lagrangians which are intrinsic to the topological field theory and composed of fermionic generators. Studying the Lagrangians through a gauge system of osp(2|2)+osp(2|2), geometrical features inherent to the algebra are revealed: a moduli space associated with the algebra is derived and the crucial roles which the fermionic generators play in the moduli space are clarified It is argued that there exists a specific relation between the topological twist and the moduli problem through a geometrical aspect of the algebra.
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arxiv:hep-th/9504135
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String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from the problem encountered in the scaling of the string tension. Unfortunately, in the usual dynamical triangulation it is not clear how to write such a term. We show that for random surfaces on a hypercubic lattice however, the analogue of the oriented self-intersection number $I[\s]$ can be defined and computed in a straightforward way. Furthermore, $I[\s]$ has a genuine topological meaning in the sense that it is invariant under the discrete analogue of continuous deformations. The resulting random surface model is no longer free and may lead to a non trivial continuum limit.
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arxiv:hep-th/9505028
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The most general electrically and magnetically charged rotating black hole solutions of 5 dimensional \KK\ theory are given in an explicit form. Various classical quantities associated with the black holes are derived. In particular, one finds the very surprising result that the gyromagnetic and gyroelectric ratios can become {\tenit arbitrarily large}. The thermodynamic quantities of the black holes are calculated and a Smarr-type formula is obtained leading to a generalized first law of black hole thermodynamics. The properties of the extreme solutions are investigated and it is shown how they naturally separate into two classes. The extreme solutions in one class are found to have two unusual properties: (i). Their event horizons have zero angular velocity and yet they have non-zero ADM angular momentum. (ii). In certain circumstances it is possible to add angular momentum to these extreme solutions without changing the mass or charges and yet still maintain an extreme solution. Regarding the extreme black holes as elementary particles, their stability is discussed and it is found that they are stable provided they have sufficient angular momentum.
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arxiv:hep-th/9505038
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Multistring vertices and the overlap identities which they satisfy are exploited to understand properties of hyperbolic Kac Moody algebras, and $E_{10}$ in particular. Since any such algebra can be embedded in the larger Lie algebra of physical states of an associated completely compactified subcritical bosonic string, one can in principle determine the root spaces by analyzing which (positive norm) physical states decouple from the $N$-string vertex. Consequently, the Lie algebra of physical states decomposes into a direct sum of the hyperbolic algebra and the space of decoupled states. Both these spaces contain transversal and longitudinal states. Longitudinal decoupling holds generally, and may also be valid for uncompactified strings, with possible consequences for Liouville theory; the identification of the decoupled states simply amounts to finding the zeroes of certain ``decoupling polynomials''. This is not the case for transversal decoupling, which crucially depends on special properties of the root lattice, as we explicitly demonstrate for a non-trivial root space of $E_{10}$. Because the $N$-vertices of the compactified string contain the complete information about decoupling, all the properties of the hyperbolic algebra are encoded into them. In view of the integer grading of hyperbolic algebras such as $E_{10}$ by the level, these algebras can be interpreted as interacting strings moving on the respective group manifolds associated with the underlying finite-dimensional Lie algebras.
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arxiv:hep-th/9505106
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For a large class of $N=2$ SCFTs, which includes minimal models and many $\s$ models on Calabi-Yau manifolds, the mirror theory can be obtained as an orbifold. We show that in such a situation the construction of the mirror can be extended to the presence of discrete torsions. In the case of the $\ZZ_2\ex\ZZ_2$ torus orbifold, discrete torsion between the two generators directly provides the mirror model. Working at the Gepner point it is, however, possible to understand this mirror pair as a special case of the Berglund--H"ubsch construction. This seems to indicate that the $\ZZ_2\ex\ZZ_2$ example is a mere coincidence, due to special properties of $\ZZ_2$ twists, rather than a hint at a new mechanism for mirror symmetry.
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arxiv:hep-th/9505120
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Based on the dispersionless KP (dKP) theory, we give a comprehensive study of the topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space.
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arxiv:hep-th/9505122
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We derive a Kontsevich-type matrix model for the c=1 string directly from the W-infinity solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the Penner and Kontsevich cases, and we study its quantum effective action. The simplicity of our model leads to an encouraging interpretation in the context of background-independent noncritical string field theory.
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arxiv:hep-th/9505127
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Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in $2+\epsilon$ dimensions. The ultraviolet stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.
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arxiv:hep-th/9505132
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We analyze the topological nature of $c=1$ string theory at the self--dual radius. We find that it admits two distinct topological field theory structures characterized by two different puncture operators. We show it first in the unperturbed theory in which the only parameter is the cosmological constant, then in the presence of any infinitesimal tachyonic perturbation. We also discuss in detail a Landau--Ginzburg representation of one of the two topological field theory structures.
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arxiv:hep-th/9505140
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We extend the construction of open descendants to the $SU(2)$ WZW models with non-diagonal left-right pairing, namely $E_7$ and the $D_{odd}$ series in the $ADE$ classification of Cappelli, Itzykson and Zuber. The structure of the resulting models is determined to a large extent by the ``crosscap constraint'', while their Chan-Paton charge sectors may be embedded in a general fashion into those of the corresponding diagonal models.
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arxiv:hep-th/9506014
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We consider the problem of constructing a non-singular inflationary universe in stringy gravity via branch changing, from a previously superexponentially expanding phase to an FRW-like phase. Our approach is based on the phase space analysis of the dynamics, and we obtain a no-go theorem which rules out the efficient scenario of branch changing catalyzed by dilaton potential and stringy fluid sources. We furthermore consider the effects of string-loop corrections to the gravitational action in the form recently suggested by Damour and Polyakov. These corrections also fail to produce the desired branch change. However, focusing on the possibility that these corrections may decouple the dilaton, we deduce that they may lead to an inflationary expansion in the presence of a cosmological constant, which asymptotically approaches Einstein-deSitter solution.
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arxiv:hep-th/9506027
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We give explicit field theoretical representations for the observables of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. To test our identification we compute some basic Wilson loop correlators reobtaining known results.
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arxiv:hep-th/9506054
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A critically discerning discussion of path integral bosonization is given. Successively evaluating the conventional path integral bosonization of QCD it is shown without any approximations that gluons must be composed of two quarks. This contradicts the fundamentals of QCD, where quarks and gluons are independent fields. Furthermore, bosonizing the Fierz reordered effective four quark interaction term yields gluons, too. Colorless ``mesons'' are shown to be Fierz equivalent to a submanifold of gluons. The results obtained are not specific to QCD, but apply to other models as well.
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arxiv:hep-th/9506055
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CP-violating phases which contribute to the electric dipole moment(EDM) of the neutron are considered in the context of orbifold compactificationof the heterotic string. In particular, we study the situation where CP is spontaneously broken by moduli fields acquiring, in general, complex expectation values at the minimum of duality invariant low energy effective potentials. We show, by explicit minimization of such a potential in the case of the ${\bf Z}_{6}-{\rm IIb}$ orbifold, that it is the presence of so called Green-Schwarz anomaly coefficients $\delta_{\rm GS}^{i} $, that leads to significant CP violating expectation values of the moduli. By evaluating the soft supersymmetry breaking moduli dependent $A$ and $B$ terms in this model, we find that the experimental bounds $\Phi (A) $, $ \Phi (B) $ $\leq 5 \times 10^{-3} $ are exceeded for a particular range of values of the auxiliary field of the $S$ modulus.
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arxiv:hep-th/9506143
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In this talk, we briefly review the basic concepts of anomalous gauge theories. It has been known for some time how theories with local anomalies can be handled. Recently it has been pointed out that global anomalies, which obstruct the quantization of certain gauge theories in the temporal gauge, get bypassed in canonical quantization.
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arxiv:hep-th/9506158
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The theory of Poisson-$\sigma$-models employs the mathematical notion of Poisson manifolds to formulate and analyze a large class of topological and almost topological two dimensional field theories. As special examples this class of field theories includes pure Yang-Mills and gravity theories, and, to some extent, the G/G gauged WZW-model. The aim of this contribution is to give a pedagogical introduction, explaining many aspects of the general theory by illustrative examples.
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arxiv:hep-th/9507020
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A large class of two-dimensional topological conformal field theories (TCFTs) are obtained by the twisting construction of Witten and Eguchi-Yang. However there seem to exist TCFTs which are not obtained in this way; for instance, TCFTs obtained from the Kazama algebra and critical string theories with generic background. We will show that by embedding the critical bosonic string into the NSR string, its TCFT can indeed be obtained by twisting a N=2 SCFT. A closer look at the construction of the N=2 superconformal algebra will show that the embedding is not essential, and this will tell us how to generalise this to other string theories. We thus conclude with the natural conjecture that _all_ TCFTs have a description as topologically twisted N=2 SCFTs. (Talk given at the Workshop on Strings, Gravity and Related Topics, held at the ICTP (Trieste, Italy) on 29-30 June, 1995.)
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arxiv:hep-th/9507024
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We develop the concept of trajectories in anyon spectra, i.e., the continuous dependence of energy levels on the kinetic angular momentum. It provides a more economical and unified description, since each trajectory contains an infinite number of points corresponding to the same statistics. For a system of non-interacting anyons in a harmonic potential, each trajectory consists of two infinite straight line segments, in general connected by a nonlinear piece. We give the systematics of the three-anyon trajectories. The trajectories in general cross each other at the bosonic/fermionic points. We use the (semi-empirical) rule that all such crossings are true crossings, i.e.\ the order of the trajectories with respect to energy is opposite to the left and to the right of a crossing.
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arxiv:hep-th/9507034
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In this report we compute the boundary states (including the boundary entropy) for the boundary sine-Gordon theory. From the boundary states, we derive both correlation and partition functions. Through the partition function, we show that boundary sine-Gordon maps onto a doubled boundary Ising model. With the current-current correlators, we calculate for finite system size the ac-conductance of tunneling quantum wires with dimensionless free conductance 1/2 (or, alternatively interacting quantum Hall edges at filling fraction 1/2). In the dc limit, the results of C. Kane and M. Fisher, Phys. Rev. B46 (1992) 15233, are reproduced.
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arxiv:hep-th/9507053
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I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
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arxiv:hep-th/9507088
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Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective 2-body interactions. This criterion may be a suitable candidate for an integrability condition.
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arxiv:hep-th/9507091
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We give the infinite-dimensional representation for the elliptic $ K $-operator satisfying the boundary Yang-Baxter equation. By restricting the functional space to finite-dimensional space, we construct the elliptic $ K $-matrix associated to Belavin's completely $ \mathbb{Z} $-symmetric $ R $-matrix.
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arxiv:hep-th/9507123
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The tracing of cosmological relics from the early string dynamics may enhance the theory and provide new perspectives on the major cosmological problems. This point is illustrated in a leading-order Bianchi-type $VII_0$ string background, wherein spatial isotropy can be claimed as such a relic. A much finer one, descending from a premordial gravitational wave, could be retrieved from its imprint on the small-scale structure of the cosmic microwave background. In spite of the absence of conventional inflation, there is no horizon problem thanks to the presence of an equally fundamental mixmaster dynamics. Implications and certain new perspectives which thus arise for the more general problem of cosmological mixing are briefly discussed.
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arxiv:hep-th/9507129
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We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to $N=2$ and $N=1$ supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged $N=1$ model. The functional forms of effective Lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic softly broken models. Nevertheless by perturbing the exact $N=1$ model results with sufficiently small soft breaking masses, we show that there exist nonsupersymmetric models that exhibit monopole condensation and confinement in the same modes as the $N=1$ case.
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arxiv:hep-th/9508002
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By studying an effective action description of the coupling of charged gauge fields in N=2 SU(n) supersymmetric Yang-Mills theories, we can describe regions of moduli space where one or more of these fields becomes unphysical. We discuss subtleties in the structure of the moduli space for SU(3).
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arxiv:hep-th/9508043
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The O(N) symmetric scalar quantum field theory with \lambda\Phi^4 interaction is discussed in the Gaussian approximation. It is shown that the Goldstone theorem is fulfilled for arbitrary N.
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arxiv:hep-th/9508087
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We analyze the collective motion of micro-organisms in the fluid and consider the problem of the red tide. The red tide is produced by the condensation of the micro-organisms, which might be a similar phenomenon to the condensation of the strings. We propose a model of the generation of the red tide. By considering the interaction between the micro- organisms mediated by the velocity fields in the fluid, we derive the Van der Waals type equation of state, where the generation of the red tide can be regarded as a phase transition from the gas of micro-organisms to the liquid. (The number density of micro-organisms which generates the red tide is order estimated.)
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arxiv:hep-th/9508112
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We study the dyon spectrum in $N=2$ Super Yang-Mills theory with gauge group $SU(2)$ coupled to $N_f$ matter multiplets in the fundamental representation. For magnetic charge one and two we determine the spectrum explicitly and show that it is in agreement with the duality predictions of Seiberg and Witten. We briefly discuss the extension to higher charge monopoles for the self-dual $N_f=4$ case and argue that the conjectured spectrum of dyons predicts the existence of certain harmonic spinors on the moduli space of higher charge monopoles.
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arxiv:hep-th/9508156
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Lorentz invariance of the current operators implies that they satisfy the well-known commutation relations with the representation operators of the Lorentz group. It is shown that if the standard construction of the current operators in quantum field theory is used then the commutation relations are broken by the Schwinger terms.
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arxiv:hep-th/9508158
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We present a brief overview of the different kinds of electromagnetic radiations expected to come from (or to be induced by) space-like sources (tachyons). New domains of radiation are here considered; and the possibility of experimental observation of tachyons via electromagnetic radiation is discussed.
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arxiv:hep-th/9508166
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It is a review of some results in Odd symplectic geometry related to the Batalin-Vilkovisky Formalism
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arxiv:hep-th/9508174
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The problem of the passage of the neutral massless particle with anomalous magnetic moment through the external electromagnetic field is considered both in pseudoclassical and quantum mechanics. The quantum description uses the hamiltonian in the Foldy--Wouthuysen representation, obtained from the pseudoclassical hamiltonian of the massive charged particle with anomalous magnetic moment in interaction with the external electromagnetic field using Weyl quantization scheme.
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arxiv:hep-th/9509038
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We obtain a bosonization prescription that allows to represent the energy-momentum tensor and supersymmetry generators of non-critical superstring theories with minimal matter as those of topological supergravity. Superstrings with $N=1$ and $N=2$ world-sheet supersymmetry are considered. The topological symmetry associated with the topological supergravity representation is studied. It is shown, in particular, that the compatibility of this topological structure with the supersymmetry enhances the superconformal symmetry of the models concerned.
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arxiv:hep-th/9509061
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I report recent studies on the evolution of perturbations in the context of the ``pre-big-bang" scenario typical of string cosmology, with emphasis on the formation of a stochastic background of relic photons and gravitons, and its possible direct/indirect observable consequences. I also discuss the possible generation of a thermal microwave background by using, as example, a simple gravi-axio-dilaton model whose classical evolution connects smoothly inflationary expansion to decelerated contraction. By including the quantum back-reaction of the produced radiation the model eventually approaches the standard radiation-dominated (constant dilaton) regime.
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arxiv:hep-th/9509127
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We derive the exact effective superpotential in 4d, N=1 supersymmetric SU(2) gauge theories with $N_A$ triplets and $2N_f$ doublets of matter superfields. We find the quantum vacua of these theories; the equations of motion (for $N_A=1$) can be reorganized into the singularity conditions of an elliptic curve. From the phase transition points to the Coulomb branch, we find the exact Abelian gauge couplings, $\tau$, for arbitrary bare masses and Yukawa couplings. We thus {\em derive} the result that $\tau$ is a section of an $SL(2,\Z)$ bundle over the moduli space and over the parameters space of bare masses and Yukawa couplings. For $N_c>2$, we derive the exact effective superpotential in branches of supersymmetric $SU(N_c)$ gauge theories with one supermultiplet in the adjoint representation ($N_A=1$) and zero or one flavor ($N_f=0,1$). We find the quantum vacua of these theories; the equations of motion can be reorganized into the singularity conditions of a genus $N_c-1$ hyperelliptic curve. Finally, we present the effective superpotential in the $N_A$, $N_f<N_c$ cases.
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arxiv:hep-th/9509130
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A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.
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arxiv:hep-th/9509147
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Whilst many solutions have been found for the Quantum Yang-Baxter Equation (QYBE), there are fewer known solutions available for its higher dimensional generalizations: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and Moore's simplex equation (FME). In this paper, we present families of solutions to FME which may help us to understand more about higher dimensional generalization of QYBE.
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arxiv:hep-th/9510010
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Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a testing ground for the application of an algebraic constraint quantization scheme which can be formulated entirely in terms of observable quantities. For the quantum mechanical reduction only the quadratic Casimir of the constraint algebra, interpreted as an observable, is needed.
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arxiv:hep-th/9510019
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We consider a 2-parameter class of solvable closed superstring models which `interpolate' between Kaluza-Klein and dilatonic Melvin magnetic flux tube backgrounds. The spectrum of string states has similarities with Landau spectrum for a charged particle in a uniform magnetic field. The presence of spin-dependent `gyromagnetic' interaction implies breaking of supersymmetry and possible existence (for certain values of magnetic parameters) of tachyonic instabilities. We study in detail the simplest example of the Kaluza-Klein Melvin model describing a superstring moving in flat but non-trivial 10-d space containing a 3-d factor which is a `twisted' product of a 2-plane and an internal circle. We also discuss the compact version of this model constructed by `twisting' the product of the two groups in SU(2) x U(1) WZNW theory without changing the local geometry (and thus the central charge). We explain how the supersymmetry is broken by continuous `magnetic' twist parameters and comment on possible implications for internal space compactification models. (Contribution to the Proceedings of the 1995 Erice School "String Gravity and Physics at the Planck Scale")
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arxiv:hep-th/9510041
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A complete analysis of the consequences of introducing a set of holonomic gauge fixing constraints (to fix the dynamics) into a singular Lagrangian is performed. It is shown in general that the dynamical system originated from the reduced Lagrangian erases all the information regarding the first class constraints of the original theory, but retains its second class. It is proved that even though the reduced Lagrangian can be singular, it never possesses any gauge freedom. As an application, the example of $n \cdot A = 0$ gauges in electromagnetism is treated in full detail.
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arxiv:hep-th/9510044
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The interplay between T-duality and supersymmetry in string theory is explored. It is shown that T-duality is always compatible with supersymmetry and simply changes a local realization to a non-local one and vice versa. Non-local realizations become natural using classical parafermions of the underlying conformal field theory. Examples presented include hyper-kahler metrics and the backgrounds for the SU(2) X U(1) and SU(2)/U(1) X U(1) X U(1) exact conformal field theories.
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arxiv:hep-th/9510103
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Models with dynamical supersymmetry breaking are interesting because they may provide a solution to both the gauge hierarchy and the fine-tuning problems. However, because of strongly interacting dynamics, it is in general impossible to analyze them quantitatively. One of the few models with calculable dynamical supersymmetry breaking is a model with SU(5) gauge symmetry and two $10$'s and two $\bar 5$'s as the matter content. We determine the ground state of this model, find the vacuum energy, reveal the symmetry breaking pattern and calculate the mass spectrum. The supertrace mass relation is exploited to verify the consistency of the calculated mass spectrum, and an accidental degeneracy is explained.
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arxiv:hep-th/9510121
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We found an infinite number of potentials surrounding 2d black hole. According to the transmission ${\cal T}$ and reflection ${\cal R}$ coefficients for scattering of string fields off 2d black hole, we can classify an infinite number of potentials into three : graviton-dilaton, tachyon and the other types. We suggest that the discrete states from all the Virasoro levels be candidates for new potentials (modes).
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arxiv:hep-th/9510123
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A lattice regularized Lax operator for the nonultralocal modified Korteweg de Vries (mKdV) equation is proposed at the quantum level with the basic operators satisfying a $q$-deformed braided algebra. Finding further the associated quantum $R$ and $Z$-matrices the exact integrability of the model is proved through the braided quantum Yang--Baxter equation, a suitably generalized equation for the nonultralocal models. Using the algebraic Bethe ansatz the eigenvalue problem of the quantum mKdV model is exactly solved and its connection with the spin-$\ha$ XXZ chain is established, facilitating the investigation of the corresponding conformal properties.
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arxiv:hep-th/9510131
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Utilizing techniques suggested by the recently obtained construction of off-shell spinning particles, we propose the arbitrary $N$-extension of supersymmetry for the KdV system. It is further suggested that the ${\aleph}_0$ extension for the SKdV system provides a paradigm for {\underline {all}} supersymmetric completely integrable systems.
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arxiv:hep-th/9510152
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Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.
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arxiv:hep-th/9510186
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For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals. For Yang-Mills theory the leading term in the expansion dominates large distance effects and leads to an area law for the Wilson loop. However, this expansion cannot be expected to converge for fields that vary more rapidly. By studying the analyticity of the vacuum functional under scale transformations we show how to re-sum this series so as to reconstruct the vacuum functional for arbitrary fields.
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arxiv:hep-th/9510188
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A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the spatio--temporal scale. Particles which are confined to small scales, i.e., do not appear in the physical spectrum, can be uncovered in this way without taking recourse to gauge fields or indefinite metric spaces. In this way notions such as quark, gluon, colour symmetry and confinement acquire a new and intrinsic meaning which is stable under gauge or duality transformations. The method is illustrated by the example of the Schwinger model.
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arxiv:hep-th/9511002
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A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and Donaldson theory and its generalizations and Seiberg-Witten invariants. Emphasis is made on the usefulness of these relations to obtain explicit expressions for topological invariants, and on the universal structure underlying both systems.
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arxiv:hep-th/9511037
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In cohomological field theory we can obtain topological invariants as correlation functions of BRS cohomology classes. A proper understanding of BRS cohomology which gives non-trivial results requires the equivariant cohomology theory. Both topological Yang-Mills theory and topological string theory are typical examples of this fact. After reviewing the role of the equivariant cohomology in topological Yang-Mills theory, we show in purely algebraic framework how the $U(1)$ equivariant cohomology in topological string theory gives the gravitational descendants. The free energy gives a generating function of topological correlation functions and leads us to consider a deformation family of cohomological field theories. In topological strings such a family is controlled by the theory of integrable system. This is most easily seen in the Landau-Ginzburg approach by looking at the contact term interactions between topological observables.
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arxiv:hep-th/9511125
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We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one dimension (quantum mechanics). Our approach starts from a Hamiltonian $H(\hat{x}, \hat{p}, \hat{\psi}, \hat{\psi}^\dagger)$ with a priori operator ordering. By inserting a finite number of complete sets of $x$ eigenstates, $p$ eigenstates and fermionic coherent states, we obtain the discretized path integral and the discretized propagators and vertices in closed form. Taking the continuum limit we read off the Feynman rules and measure of the continuum theory which differ from those often assumed. In particular, mode regularization of the continuum theory is shown in an example to give incorrect results. As a consequence of time-slicing, the action and Feynman rules, although without any ambiguities, are necessarily noncovariant, but the final results are covariant if $\hat{H}$ is covariant. All our derivations are exact. Two loop calculations confirm our results.
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arxiv:hep-th/9511141
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We analyze nonabelian massive Higgs-free theories in the causal Epstein-Glaser approach. Recently, there has been renewed interest in these models. In particular we consider the well-known Curci-Ferrari model and the nonabelian St\"uckelberg models. We explicitly show the reason why the considered models fail to be unitary. In our approach only the asymptotic (linear) BRS-symmetry has to be considered.
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arxiv:hep-th/9511176
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The SL(2,R) WZW model, one of the simplest models for strings propagating in curved space time, was believed to be non-unitary in the algebraic treatment involving affine current algebra. It is shown that this was an error that resulted from neglecting a zero mode that must be included to describe the correct physics of non-compact WZW models. In the presence of the zero mode the mass-shell condition is altered and unitarity is restored. The correct currents, including the zero mode, have logarithmic cuts on the worldsheet. This has physical consequences for the spectrum because a combination of zero modes must be quantized in order to impose periodic boundary conditions on mass shell in the physical sector. To arrive at these results and to solve the model completely, the SL(2,R) WZW model is quantized in a free field formalism that differs from previous ones in that the fields and the currents are Hermitean, there are cuts, and there is a new term that could be present more generally, but is excluded in the WZW model.
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arxiv:hep-th/9511187
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It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.
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arxiv:hep-th/9511189
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We construct a non-perturbative, single-valued solution for the metric and the motion of $N$ interacting particles in $2+1$-Gravity. The solution is explicit for two particles with any speed and for any number of particles with small speed. It is based on a mapping from multivalued Minkowskian coordinates to single-valued ones, which solves the non-abelian monodromies due to particles' momenta. The two and three-body cases are treated in detail.
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arxiv:hep-th/9511207
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In this note we show that the single soliton solutions known previously in the $1+1$ dimensional affine Toda field theories from a variety of different methods \cite{H1,MM,OTUa,OTUb}, are in fact not the most general single soliton solutions. We exhibit single soliton solutions with additional small parameters which reduce to the previously known solutions when these extra parameters are set to zero. The new solution has the same mass and topological charges as the standard solution when these parameters are set to zero. However we cannot yet completely rule out the possibility that other solutions with larger values of these extra parameters are non-singular, in the cases where the number of extra parameters is greater than one, and if so their topological charges would most likely be different.
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arxiv:hep-th/9511225
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We consider a certain local generalization of BRS transformations of Yang-Mills theory in which the anti-commuting parameter is space time dependent. While these are not exact symmetries, they do lead to a new nontrivial WT identity. We make a precise connection between the ``local BRS "and the broken orthosymplectic symmetry recently found in superspace formulation of Yang-Mills theory by showing that the local BRS WT identity is precisely the WT identity obtained in the superspace formulation via a superrotation. This ``local BRS " WT identity could lead to new consequences not contained in the usual BRS WT identity.
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arxiv:hep-th/9512033
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We define a complete set of supertraces on the algebra $SH_N(\nu)$, the algebra of observables of the $N$-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of $N=1$ and $N=2$ to arbitrary $N$. It is shown that $SH_N(\nu)$ admits $q(N)$ independent supertraces where $q(N)$ is a number of partitions of $N$ into a sum of odd positive integers, so that $q(N)>1$ for $N\ge 3$. Some consequences of the existence of several independent supertraces of $SH_N (\nu )$ are discussed such as the existence of ideals in associated $W_{\infty}$ - type Lie superalgebras.
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arxiv:hep-th/9512038
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It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate ``area " law.
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arxiv:hep-th/9512047
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The modular transformations of the $(1|1)$ complex supermanifolds in the like-Schottky modular parameterization are discussed. It is shown that these "supermodular" transformations depend on the spinor structure of the supermanifold by terms proportional to the odd modular parameters. The above terms are calculated in the explicit form. They are urgent for the divergency problem in the Ramond-Neveu-Schwarz superstring theory and for calculating the fundamental domain in the modular space. The supermodular transformations of the multi-loop superstring partition functions calculated by the solution of the Ward identities are studied. The above Ward identities are shown to be covariant under the supermodular transformations. So the partition functions necessarily possess the covariance under the transformations discussed. It is demonstrated explicitly the covariance of the above partition functions at zero odd moduli under those supermodular transformations, which turn a pair of even genus-1 spinor structures to a pair of the odd genus-1 spinor ones. The brief consideration of the cancellation of divergences is given.
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arxiv:hep-th/9512057
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Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold $G$ are dual to $D$-brane - anti-$D$-brane pairs propagating on the dual group manifold $\ti G$. The $D$-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group $\ti G$ by the dressing action of the group $G$. T-duality maps the momentum of the open string into the mutual distance of the $D$-branes in the pair. The whole picture is then extended to the full modular space $M(D)$ of the Poisson-Lie equivalent $\si$-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of $D$-branes living on targets belonging to $M(D)$. In this more general case the $D$-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.
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arxiv:hep-th/9512124
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Global N=2 supersymmetry in four dimensions with a gauged central charge is formulated in superspace. To find an irreducible representation of supersymmetry for the gauge connections a set of constraints is given. Then the Bianchi identities are solved subject to this set of constraints. It is shown that the gauge connection of the central charge is a N=2 vector multiplet. Moreover the Bogomol'nyi bound of the massive particle states is studied.
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arxiv:hep-th/9512165
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In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.
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arxiv:hep-th/9601128
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We construct Landau-Ginzburg Lagrangians for minimal bosonic ($N=0$) $W$-models perturbed with the least relevant field, inspired by the theory of $N=2$ supersymmetric Landau-Ginzburg Lagrangians. They agree with the Lagrangians for unperturbed models previously found with Zamolodchikov's method. We briefly study their properties, e.g. the perturbation algebra and the soliton structure. We conclude that the known properties of $N=2$ solitons (BPS, lines in $W$ plane, etc.) hold as well. Hence, a connection with a generalized supersymmetric structure of minimal $W$-models is conjectured.
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arxiv:hep-th/9602001
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We construct compact examples of D-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12 dimensional `F-theory'. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold $K$ which admits elliptic fibration is equivalent to compactification of F-theory on $K\times S^1$. A large class of $N=1$ theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of F-theory is on $Spin(7)$ holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten's proposal for solving the cosmological constant problem in four dimensions.
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arxiv:hep-th/9602022
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We review the application of bosonic string techniques to the calculation of renormalization constants and effective actions in Yang-Mills theory. We display the multiloop string formulas needed to compute Yang-Mills amplitudes, and we discuss how the renormalizations of proper vertices can be extracted in the field theory limit. We show how string techniques lead to the background field method in field theory, and indicate how the gauge invariance of the multiloop effective action can be inferred form the string formalism. (Proceedings of the 29th International Symposium on the Theory of Elementary Particles, Buckow (Germany), Aug.-Sept. 1995. Preprint DFTT 04/96)
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arxiv:hep-th/9602056
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We consider $E_8\times E_8$ heterotic compactifications on $K3$ and $K3\times T^2$. The idea of heterotic/heterotic duality in $D=6$ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $E_8$'s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to $D=4$, we find that the duals in the DMW case correspond to $N=2$ models in which the $\beta$-function of the different group factors verify ${\beta }_\alpha=12$, whereas the asymmetric solutions that we propose have ${\beta }_\alpha=24$. We check the consistency of these dualities by studying the different large $T,S$ limits of the gauge kinetic function. Dual $N=1$, $D=4$ models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.
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arxiv:hep-th/9602097
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We study compactifications of F-theory on certain Calabi--Yau threefolds. We find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get promoted to $N=1$ dualities between heterotic string and F-theory in 6 dimensions. The six dimensional heterotic/heterotic duality becomes a classical geometric symmetry of the Calabi--Yau in the F-theory setup. Moreover the F-theory compactification sheds light on the nature of the strong coupling transition and what lies beyond the transition at finite values of heterotic string coupling constant.
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arxiv:hep-th/9602114
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A supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. This formulation generalizes the known action for scalar charged particles investigated in papers by Fokker, Schwarzschild, Tetrode, Wheeler and Feynman. The superfield formulation of the electrodynamics of the Maxwell supermultiplet, constructed from the world coordinates of charged or neutral fermions is carried out basing on the proposed action.
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arxiv:hep-th/9602128
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We present here our considerations concerning the problem of classical consistency of pseudoclassical models touched upon in a recent comment on our paper "New pseudoclassical model for Weyl particle".
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arxiv:hep-th/9602151
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$SU(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of level $k$ (an integer) added, has two dimensionful coupling constants, $g^2 k$ and $g^2 N$; its possible phases depend on the size of $k$ relative to $N$. For $k \gg N$, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For $k=0$, the theory is badly infrared singular in perturbation theory, a non-perturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of $k$, called $k_c$, with $k_c/N \approx 2 \pm .7$. Three lines of evidence are given: First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if $k \leq 29N/12$.The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the $k=0$ case. Second, we study in a rough approximation the free energy and show that for $k \leq k_c$ there is a non-trivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass $M$, while both the condensate and $M$ vanish for $k \geq k_c$. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass $m$ and a (gauge-invariant) dynamical mass $M$. We show that if $M \gsim 0.5 m$, there are finite-action quantum sphalerons, while none survive in the classical limit $M=0$, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as $M \rightarrow 0$.
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arxiv:hep-th/9602157
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Within the Euclidean path integral and mass perturbation theory we derive, from the Dyson-Schwinger equations of the massive Schwinger model, a general formula that incorporates, for sufficiently small fermion mass, all the bound-state mass poles of the massive Schwinger model. As an illustration we perturbatively compute the masses of the three lowest bound states.
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arxiv:hep-th/9602175
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We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with tensionless strings are sometimes phase transition points between different phases of the theory. These results appear to connect all known $N=1$ supersymmetric six-dimensional vacua.
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arxiv:hep-th/9603003
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The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting $N=2$ supergravity as low energy limit.
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arxiv:hep-th/9603004
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The covariant path integral for chiral bosons obtained by McClain, Wu and Yu is generalized to chiral p-forms. In order to handle the reducibility of the gauge transformations associated with the chiral p-forms and with the new variables (in infinite number) that must be added to eliminate the second class constraints, the field-antifield formalism is used.
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arxiv:hep-th/9603031
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A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied to more general cases, is developed for that chain. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations different from that for a homogeneous chain. A conjecture about the form of the solutions for more general chains is presented. PACS: 75.10.Jm, 05.50+q 02.20 Sv
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arxiv:hep-th/9603046
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In this paper, we present a parity-preserving QED3 with spontaneous breaking of a local U(1)-symmetry. The breaking is accomplished by a potential of the \vf^6-type. It is shown that a net attractive interaction appears in the M{\o}ller scattering (s and p-wave scattering between two electrons) as mediated by the gauge field and a Higgs scalar. This might favour a pair-condensation mechanism.
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arxiv:hep-th/9603054
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We derive parts of the monopole and dyon spectra for N=2 super-Yang--Mills theories in four dimensions with gauge groups G of rank r>1 and matter multiplets. Special emphasis is put on G=SU(3) and those matter contents that yield perturbatively finite theories. There is no direct interpretation of the soliton spectra in terms of naive selfduality under strong--weak coupling and exchange of electric and magnetic charges. We argue that, in general, the standard procedure of finding the dyon spectrum will not give results that support a conventional selfduality hypothesis --- the SU(2) theory with four fundamental hypermultiplets seems to be an exception. Possible interpretations of the results are discussed.
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arxiv:hep-th/9603134
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The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature connected with noncommuting random variables. In the context of large-N hermitian matrices, it means that the the multi-matrix model considered contains no bias with respect to the relative orientations of the matrices. In such a gauge background, the spectrum of a colored particle can be solved for analytically. In three dimensions, near zero momentum, the energy distribution for the spinless particle displays a gap, while the energy distribution for the particle with spin does not.
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arxiv:hep-th/9604012
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We show how the method of separation of variables can be used to construct integrable models corresponding to curves describing vacuum structure of four-dimensional ${\cal N} = 2$ SUSY Yang-Mills theories. We use this technique to construct models corresponding to $SU(N)$ Yang-Mills theory with $N_f<2N$ matter hypermultiplets by generalising the periodic Toda lattice. We also show that some special cases of massive $SU(3)$ gauge theory can be equivalently described by the generalisations of the Goryachev-Chaplygin top obtained via separation of variables.
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arxiv:hep-th/9604101
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By using the brick wall method we calculate the thermodynamic potential of the complex scalar field in a charged Kerr black hole. Using it we show that in the Hartle-Hawking state the leading term of the entropy is proportional to $\frac{ A _H}{\epsilon^2}$, which becomes divergent as the system approaches the black hole horizon. The origin of the divergence is that the density of states diverges at the horizon.
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arxiv:hep-th/9604130
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We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible $N=2$ supersymmetric integrable hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the $N=2$ supersymmetric extensions of the Generalized Non-Linear Schr\"{o}dinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct hamiltonians we are led to a new definition of super-residues for degenerate N=2 supersymmetric pseudodifferential operators. We have found a new non-polinomial Miura-like realization for $N=2$ superconformal algebra in terms of two bosonic chiral--anti--chiral free superfields.
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arxiv:hep-th/9604165
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I review how traditional grand unified theories, which require adjoint (or higher representation) Higgs fields for breaking to the standard model, can be contained within string theory. The status (as of January 1996) of the search for stringy free fermionic three generation SO(10) SUSY--GUT models is discussed. Progress in free fermionic classification of both SO(10)$_2$ charged and uncharged embeddings and in $N=1$ spacetime solutions is presented. Based on talks presented at the Workshop on SUSY Phenomena and SUSY GUTs, Santa Barbara, California, Dec. 7-11, 1995, and at the Orbis Scientiae, Coral Gables, Florida, January 25-28, 1996. Appearing in the Proceedings of Orbis Scientiae, 1996.
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arxiv:hep-th/9604183
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A parquet approximation (generalized ladder diagrams) in matrix models is considered. By means of numerical calculations we demonstrate that in the large $N$ limit the parquet approximation gives an excellent agreement with exact results.
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arxiv:hep-th/9605005
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We consider 4D quantum gravity with N-dilatons with the most general couplings. Especially, on constant dilaton and arbitrary metric background, we show the structure of the divergent terms. We show the constraint between the couplings necessary to cancel the coefficient of the square of the Wyle tensor. Next we show the N dependence of a non-renormalizable divergent term, and found that it cannot be canceled in the case of $N \geq 1$ with any fine-tuning of the couplings.
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arxiv:hep-th/9605025
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The infrared dynamics in the (3+1)-dimensional supersymmetric and non-supersymmetric Nambu-Jona-Lasinio model in a constant magnetic field is studied. While at strong coupling the dynamics in these two models is essentially different, it is shown that the models become equivalent at weak coupling. In particular, at weak coupling, as the strength of the magnetic field goes to infinity, both the supersymmetric and non-supersymmetric Nambu-Jona-Lasinio models are reduced to a continuum set of independent (1+1)-dimensional Gross-Neveu models, labeled by the coordinates in the plane perpendicular to the magnetic field. The relevance of these results for cosmological models based on supersymmetric dynamics is pointed out.
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arxiv:hep-th/9605027
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Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.
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arxiv:hep-th/9605067
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Presented is an integral formula for solutions to the quantum Knizhnik--Zamolodchikov equation of level $0$ associated with the vector representation of $U_q (\widehat{ sl_n})$. This formula gives a generalization of both our previous work for $U_q (\widehat{ sl_2})$ and Smirnov's formula for form factors of $SU(n)$ chiral Gross-Neveu model.
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arxiv:hep-th/9605123
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We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W-infinity algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with U(1)xSU(m) affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.
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arxiv:hep-th/9605127
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Chern-Simons-Matter Lagrangian with noncompact gauge symmetry group is considered. The theory is quantized in the holomorphic gauge with a complex gauge fixing condition. The model is discussed, in which the the gauge and matter fields are accompanied by the complex conjugate counterparts. It is argued, that such a theory represents an adequate framework for the description of the quantum Hall states.
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arxiv:hep-th/9605160
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Based on the covariant background field method, we calculate the ultraviolet counter\-terms up to two-loop order and discuss the renormalizability of the three-dimensional non-linear sigma models with arbitrary Riemannian manifolds as target spaces. We investigate the bosonic model and its supersymmetric extension. We show that at the one-loop level these models are renormalizable and even finite when the manifolds are Ricci-flat. However, at the two-loop order, we find non-renormalizable counterterms in all cases considered, so the renormalizability and finiteness of such models are completely lost in this order.
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arxiv:hep-th/9605198
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It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order `structure constants') which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra.
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arxiv:hep-th/9605213
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In four dimensions there are 4 different types of extremal Maxwell/scalar black holes characterized by a scalar coupling parameter $a$ with $a=0,1/\sqrt{3} , 1 , \sqrt{3}$. These black holes can be described as intersections of ten--dimensional non-singular Ramond-Ramond objects, i.e.~$D$-branes, waves and Taub-NUT solitons. Using this description it can be shown that the four--dimensional black holes decompactify near the core to higher--dimensional {\em non-singular} solutions. In terms of these higher--dimensional non-singular solutions we define a non-vanishing entropy for all four black hole types from a four--dimensional point of view.
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arxiv:hep-th/9605216
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The complexified gauging of the de Sitter group gives a unified theory for the electroweak and gravitational interactions. The standard spectrum for the electroweak gauge bosons is recovered with the correct mass assignments, following a spontaneous breaking of the gauge symmetry imposed by the geometry. There is no conventional Higgs sector. New physics is predicted with gravity-induced electroweak processes (at the electroweak and at an intermediate scale of about $10^{10}Gev$) as well as with novel-type of effects (such as gravitational Aharonov-Bohm and violations of the Principle of equivalence to 1 part in $10^{17}$). The new theoretical perspectives emerging from this geometric unification are briefly discussed.
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arxiv:hep-th/9605217
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