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Magnetically charged dilatonic black holes have a perturbatively infinite ground state degeneracy associated with an infinite volume throat region of the geometry. A simple argument based on causality is given that these states do not have a description as ordinary massive particles in a low-energy effective field theory. Pair production of magnetic black holes in a weak magnetic field is estimated in a weakly-coupled semiclassical expansion about an instanton and found to be finite, despite the infinite degeneracy of states. This suggests that these states may store the information apparently lost in black hole scattering processes.
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arxiv:hep-th/9211030
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We consider a continuous model of D-dimensional elastic (polymerized) manifold fluctuating in d-dimensional Euclidean space, interacting with a single impurity via an attractive or repulsive delta-potential (but without self-avoidance interactions). Except for D=1 (the polymer case), this model cannot be mapped onto a local field theory. We show that the use of intrinsic distance geometry allows for a rigorous construction of the high-temperature perturbative expansion and for analytic continuation in the manifold dimension D. We study the renormalization properties of the model for 0<D<2, and show that for d<d* where d*=2D/(2-D) is the upper critical dimension, the perturbative expansion is UV finite, while UV divergences occur as poles at d=d*. The standard proof of perturbative renormalizability for local field theories (the BPH theorem) does not apply to this model. We prove perturbative renormalizability to all orders by constructing a subtraction operator based on a generalization of the Zimmermann forests formalism, and which makes the theory finite at d=d*. This subtraction operation corresponds to a renormalization of the coupling constant of the model (strength of the interaction with the impurity). The existence of a Wilson function, of an epsilon-expansion around the critical dimension, of scaling laws for d<d* in the repulsive case, and of non-trivial critical exponents of the delocalization transition for d>d* in the attractive case is thus established. To our knowledge, this provides the first proof of renormalizability for a model of extended objects, and should be applicable to the study of self-avoidance interactions for random manifolds.
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arxiv:hep-th/9211038
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We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individual conformal field theory factors have been classified. We illustrate the use of these constraints for theories of the type $SU(2)_{K_A}\otimes SU(2)_{K_B}$, finding all consistent theories for $K_A,K_B$ odd. Second we show how known diagonal modular invariants can be used to construct some inherently asymmetric ones where the holomorphic and anti-holomorphic theories do not share the same chiral algebra. Some explicit examples are given.
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arxiv:hep-th/9211073
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We treat the horizons of charged, dilaton black extended objects as quantum mechanical objects. We show that the S matrix for such an object can be written in terms of a p-brane-like action. The requirements of unitarity of the S matrix and positivity of the p-brane tension equivalent severely restrict the number of space-time dimensions and the allowed values of the dilaton parameter a. Generally, black objects transform at the extremal limit into p-branes.
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arxiv:hep-th/9211117
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We present simple, analytic solutions to the Einstein-Maxwell equation, which describe an arbitrary number of charged black holes in a spacetime with positive cosmological constant $\Lambda$. In the limit $\Lambda=0$, these solutions reduce to the well known Majumdar-Papapetrou (MP) solutions. Like the MP solutions, each black hole in a $\Lambda >0$ solution has charge $Q$ equal to its mass $M$, up to a possible overall sign. Unlike the $\Lambda = 0$ limit, however, solutions with $\Lambda >0$ are highly dynamical. The black holes move with respect to one another, following natural trajectories in the background deSitter spacetime. Black holes moving apart eventually go out of causal contact. Black holes on approaching trajectories ultimately merge. To our knowledge, these solutions give the first analytic description of coalescing black holes. Likewise, the thermodynamics of the $\Lambda >0$ solutions is quite interesting. Taken individually, a $|Q|=M$ black hole is in thermal equilibrium with the background deSitter Hawking radiation. With more than one black hole, because the solutions are not static, no global equilibrium temperature can be defined. In appropriate limits, however, when the black holes are either close together or far apart, approximate equilibrium states are established.
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arxiv:hep-th/9212035
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We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.
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arxiv:hep-th/9212094
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We prove new identities betweenthe values of Rogers dilogarithm function and describe a connection between these identities and spectra in conformal field theory.
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arxiv:hep-th/9212150
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We study duality transformations for two-dimensional sigma models with abelian chiral isometries and prove that generic such transformations are equivalent to integrated marginal perturbations by bilinears in the chiral currents, thus confirming a recent conjecture by Hassan and Sen formulated in the context of Wess-Zumino-Witten models. Specific duality transformations instead give rise to coset models plus free bosons.
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arxiv:hep-th/9301005
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We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the nonperturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.
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arxiv:hep-th/9301017
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Physical states of two-dimensional topological gauge theories are studied using the BRST formalism in the light-cone gauge. All physical states are obtained for the abelian theory. There are an infinite number of physical states with different ghost numbers. Simple examples of physical states in a non-abelian theory are also given.
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arxiv:hep-th/9301027
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In this talk new formulations of the Green--Schwarz heterotic strings in $D$ dimensions that involve commuting spinors, are reviewed. These models are invariant under $n$--extended, world sheet supersymmetry as well as under $N=1$, target space supersymmetry where $n\leq D-2$ and $D=3,4,6,10$. The world sheet supersymmetry replaces $n$ components (and provides a geometrical meaning) of the $\kappa$--symmetry in the Green--Schwarz approach. The models in $D=10$ for $n=1,2,8$ are discussed explicitly.
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arxiv:hep-th/9301055
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We employ the conformal bootstrap to re-examine the problem of finding the critical behavior of four-Fermion theory at its strong coupling fixed point. Existence of a solution of the bootstrap equations indicates self-consistency of the assumption that, in space-time dimensions less than four, the renormalization group flow of the coupling constant of a four-Fermion interaction has a nontrivial fixed point which is generally out of the perturbative regime. We exploit the hypothesis of conformal invariance at this fixed point to reduce the set of the Schwinger-Dyson bootstrap equations for four-Fermion theory to three equations which determine the scale dimension of the Fermion field $\psi$, the scale dimension of the composite field $\bar{\psi}\psi$ and the critical value of the Yukawa coupling constant. We solve the equations assuming this critical value to be small. We show that this solution recovers the fixed point for the four-fermion interaction with $N$-component fermions in the limit of large $N$ at (Euclidean) dimensions $d$ between two and four. We perform a detailed analysis of the $1/N$-expansion in $d=3$ and demonstrate full agreement with the conformal bootstrap. We argue that this is a useful starting point for more sophisticated computations of the critical indices.
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arxiv:hep-th/9301069
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We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We used longer runs than previous simulations and give new and more accurate estimates of critical exponents. Our data indicate a cusp singularity in the specific heat. The transition temperature, as well as the exponents are topology dependent.
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arxiv:hep-th/9302025
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We discuss the structure of correlators involving the spinor emission vertex in non critical $N=1$ superstring theory. The technique used in the computation is the zero mode integration to arrive at the integral representation, and later an analysis of the pole structure of the integrals which are thus obtained. Our analysis has been done primarily for the 5-point functions. The result confirms previous expectations and prepares ground for a comparison with computations using matrix models techniques.
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arxiv:hep-th/9302032
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There is substancial overlap with hepth-9211081. More results are presented for duality in the non-compact case. It is argued that duality persists as a symmetry also in that case.
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arxiv:hep-th/9302033
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The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables is considered and it is shown that the classical equations of motion are exactly integrated in coordinate system determined by components of 2D torsion. For some choice of integrating constant the solution is of the charged black hole type. The conserved charge and ADM mass of the black hole are calculated.
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arxiv:hep-th/9302040
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Recently a new supersymmetric extension of the KdV hierarchy has appeared in a matrix-model-inspired approach to $2{-}d$ quantum supergravity. Here we prove that this hierarchy is essentially the KdV hierarchy, where the KdV field is now replaced by an even superfield. This allows us to find the conserved charges and the bihamiltonian structure, and to prove its integrability. We also extend the hierarchy by odd flows in a supersymmetric fashion.
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arxiv:hep-th/9302057
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A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the geometric consequences of the fact that certain cohomology groups of super Riemann surfaces are not freely generated modules. The divisor theory of Rosly, Schwarz, and Voronov gives a map from a supertorus to its Picard group, but this map is a projection, not an isomorphism as it is for ordinary tori. The geometric realization of the addition law on Pic via intersections of the supertorus with superlines in projective space is described. The isomorphisms of Pic with the Jacobian and the divisor class group are verified. All possible isogenies, or surjective holomorphic maps between supertori, are determined and shown to induce homomorphisms of the Picard groups. Finally, the solutions to the new super Kadomtsev-Petviashvili (super KP) hierarchy of Mulase-Rabin which arise from super elliptic curves via the Krichever construction are exhibited.
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arxiv:hep-th/9302105
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Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32\pi$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.
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arxiv:hep-th/9303006
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We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limit provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator as recently discussed by Leutwyler and Smilga.
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arxiv:hep-th/9303012
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The ground state density matrix for a massless free field is traced over the degrees of freedom residing inside an imaginary sphere; the resulting entropy is shown to be proportional to the area (and not the volume) of the sphere. Possible connections with the physics of black holes are discussed.
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arxiv:hep-th/9303048
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We discuss two classes of exact (in $\a'$) string solutions described by conformal sigma models. They can be viewed as two possibilities of constructing a conformal model out of the non-conformal one based on the metric of a $D$-dimensional homogeneous $G/H$ space. The first possibility is to introduce two extra dimensions (one space-like and one time-like) and to impose the null Killing symmetry condition on the resulting $2+D$ dimensional metric. In the case when the ``transverse" model is $n=2$ supersymmetric and the $G/H$ space is K\"ahler-Einstein the resulting metric-dilaton background can be found explicitly. The second possibility - which is realised in the sigma models corresponding to $G/H$ conformal theories - is to deform the metric, introducing at the same time a non-trivial dilaton and antisymmetric tensor backgrounds. The expressions for the metric and dilaton in this case are derived using the operator approach in which one identifies the equations for marginal operators of conformal theory with the linearised (near a background) expressions for the `$\b$-functions'. Equivalent results are then reproduced in the direct field-theoretical approach based on computing first the effective action of the $G/H$ gauged WZW model and then solving for the $2d$ gauge field. Both the bosonic and the supersymmetric cases are discussed. ( To be published in the Proceedings of the 26 Workshop ``From Superstrings to Supergravity", Erice, 5-12 December,1992.)
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arxiv:hep-th/9303054
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Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with non--supersymmetric particle content and vanishing one-- and two--loop beta functions for the gauge coupling and one--loop beta functions for Yukawa--couplings is presented.
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arxiv:hep-th/9303151
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We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian equations of motion. Connection between the lattice Faddeev-Takhtadjan-Volkov algebra [1] and q-deformed Virasoro is also discussed.
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arxiv:hep-th/9303166
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We considered a charged quantum mechanical particle with spin ${1\over 2}$ and gyromagnetic ratio $g\ne 2$ in the field af a magnetic string. Whereas the interaction of the charge with the string is the well kown Aharonov-Bohm effect and the contribution of magnetic moment associated with the spin in the case $g=2$ is known to yield an additional scattering and zero modes (one for each flux quantum), an anomaly of the magnetic moment (i.e. $g>2$) leads to bound states. We considered two methods for treating the case $g>2$. \\ The first is the method of self adjoint extension of the corresponding Hamilton operator. It yields one bound state as well as additional scattering. In the second we consider three exactly solvable models for finite flux tubes and take the limit of shrinking its radius to zero. For finite radius, there are $N+1$ bound states ($N$ is the number of flux quanta in the tube).\\ For $R\to 0$ the bound state energies tend to infinity so that this limit is not physical unless $g\to 2$ along with $R\to 0$. Thereby only for fluxes less than unity the results of the method of self adjoint extension are reproduced whereas for larger fluxes $N$ bound states exist and we conclude that this method is not applicable.\\ We discuss the physically interesting case of small but finite radius whereby the natural scale is given by the anomaly of the magnetic moment of the electron $a_e=(g-2)/2\approx 10^{-3}$.
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arxiv:hep-th/9304017
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Motivated by the problem of background independence of closed string field theory we study geometry on the infinite vector bundle of local fields over the space of conformal field theories (CFT's). With any connection we can associate an excluded domain $D$ for the integral of marginal operators, and an operator one-form $\omega_\mu$. The pair $(D, \omega_\mu)$ determines the covariant derivative of any correlator of local fields. We obtain interesting classes of connections in which $\omega_\mu$'s can be written in terms of CFT data. For these connections we compute their curvatures in terms of four-point correlators, $D$, and $\omega_\mu$. Among these connections three are of particular interest. A flat, metric compatible connection $\HG$, and connections $c$ and $\bar c$ having non-vanishing curvature, with $\bar c$ being metric compatible. The flat connection cannot be used to do parallel transport over a finite distance. Parallel transport with either $c$ or $\bar c$, however, allows us to construct a CFT in the state space of another CFT a finite distance away. The construction is given in the form of perturbation theory manifestly free of divergences.
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arxiv:hep-th/9304053
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A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method is used to calculate q - deformed Clebsch - Gordan coefficients. The connection with covariant oscillators and irreducible tensor operators is established. This approach can be extended to other quantum groups.
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arxiv:hep-th/9304073
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All classical Lie algebras can be realized \`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter $q$ is a phase related to the anyonic statistical parameter. A crucial r\^ole in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case $q$ can also be real.
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arxiv:hep-th/9304108
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Usual coset construction $\SU{k}\times\SU{l}/\SU{k+l}$ of Wess--Zumino conformal field theory is presented as a coset construction of minimal models. This new coset construction can be defined rigorously and allows one to calculate easily correlation functions of a number of primary fields.
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arxiv:hep-th/9304116
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The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the field strengths, are essential in the construction of $q$-deformed gauge theories. An explicit expression $\om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l$ for the $q$-commutations of left-invariant one-forms is found, with $\Z{ij}{kl} \om^k \we \om^l \qonelim \om^j\we\om^i$.
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arxiv:hep-th/9304161
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A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
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arxiv:hep-th/9305009
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Static black holes in two-dimensional string theory can carry tachyon hair. Configurations which are non-singular at the event horizon have non-vanishing asymptotic energy density. Such solutions can be smoothly extended through the event horizon and have non-vanishing energy flux emerging from the past singularity. Dynamical processes will not change the amount of tachyon hair on a black hole. In particular, there will be no tachyon hair on a black hole formed in gravitational collapse if the initial geometry is the linear dilaton vacuum. There also exist static solutions with finite total energy, which have singular event horizons. Simple dynamical arguments suggest that black holes formed in gravitational collapse will not have tachyon hair of this type.
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arxiv:hep-th/9305030
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The affine-Virasoro Ward identities are a system of non-linear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward identities in some detail, with several central results. First, we solve for the correlators of the affine-Sugawara nests, which are associated to the nested subgroups $g\supset h_1 \supset \ldots \supset h_n$. We also find an equivalent algebraic formulation which allows us to find global solutions across the set of all affine-Virasoro constructions. A particular global solution is discussed which gives the correct nest correlators, exhibits braiding for all affine-Virasoro correlators, and shows good physical behavior, at least for four-point correlators at high level on simple $g$. In rational and irrational conformal field theory, the high-level fusion rules of the broken affine modules follow the Clebsch-Gordan coefficients of the representations.
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arxiv:hep-th/9305072
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We show that the bosonic string theory quantized in the Beltrami parametrization possesses a supersymmetric structure like the vector-supersymmetry already observed in topological field theories.
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arxiv:hep-th/9305148
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It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on pre- and post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of the impossibility of realistic Lorentz invariant interpretation of quantum theory (without assumption of locality) is discussed.
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arxiv:hep-th/9305162
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New development of the theory of Grothendieck polynomials, based on an exponential solution of the Yang-Baxter equation in the algebra of projectors are given.
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arxiv:hep-th/9306005
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The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.
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arxiv:hep-th/9306017
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The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact $N$-anyon groundstates, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter $\alpha\in[-1,0]$ where a gap exists. Interestingly enough, one finds that at the critical filling $\nu=-{1/\alpha}$ where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.
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arxiv:hep-th/9306039
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Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.
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arxiv:hep-th/9306042
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We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum mechanical potentials. By considering the most general possible time-dependent re-definition of the spatial coordinate, as well as general transformations on the wavefunctions, we show that separation of variables applies and exact solubility occurs only in a very restricted class of time-dependent models. We consider the formal structure underlying our findings, and the relationship between our results and other work on time-dependent potentials. As an application of our methods, we apply our results to the calculations of propagators.
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arxiv:hep-th/9306060
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After pointing out the role of the compactification lattice for spectrum calculations in orbifold models, I discuss modular discrete symmetry groups for $Z_N$ or\-bi\-folds. I consider the $Z_7$ orbifold as a nontrivial example of a (2,2) model and give the generators of the modular group for this case, which does not contain $[SL(2,{\bf Z})]^3$ as had been speculated. I also discuss how to treat cases where quantized Wilson lines are present. I consider in detail an example, demonstrating that quantized Wilson lines affect the modular group in a nontrivial manner. In particular, I show that it is possible for a Wilson line to break $SL(2,{\bf Z})$.}
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arxiv:hep-th/9306074
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Recently, a class of interaction round the face (IRF) solvable lattice models were introduced, based on any rational conformal field theory (RCFT). We investigate here the connection between the general solvable IRF models and the fusion ones. To this end, we introduce an associative algebra associated to any graph, as the algebra of products of the eigenvalues of the incidence matrix. If a model is based on an RCFT, its associated graph algebra is the fusion ring of the RCFT. A number of examples are studied. The Gordon--generalized IRF models are studied, and are shown to come from RCFT, by the graph algebra construction. The IRF models based on the Dynkin diagrams of A-D-E are studied. While the $A$ case stems from an RCFT, it is shown that the $D-E$ cases do not. The graph algebras are constructed, and it is speculated that a natural isomorphism relating these to RCFT exists. The question whether all solvable IRF models stems from an RCFT remains open, though the $D-E$ cases shows that a mixing of the primary fields is needed.
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arxiv:hep-th/9306143
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T-Duality invariant worldsheet string actions, recently written down by Schwarz and Sen, are coupled to the worldsheet gauge fields. It is shown that the integration of the dual coordinates gives the conventional, vector, axial and chiral, gauged string actions for the appropriate choice of the gauged isometries. Alternatively, the gauge field integration is shown to give a T-duality invariant action which matches with the corresponding results known earlier.
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arxiv:hep-th/9306151
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Two types of semiclassical calculations have been used to study quantum effects in black hole backgrounds, the WKB and the mean field approaches. In this work we systematically reconstruct the logical implications of both methods on quantum black hole physics and provide the link between these two approaches. Our conclusions completely support our previous findings based solely on the WKB method: quantum black holes are effectively p-brane excitations and, consequently, no information loss paradox exists in this problem.
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arxiv:hep-th/9307104
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We present the formalism for computing the critical exponent corresponding to the $\beta$-function of the Nambu--Jona-Lasinio model with $SU(M)$ $\times$ $SU(M)$ continuous chiral symmetry at $O(1/N^2)$ in a large $N$ expansion, where $N$ is the number of fermions. We find that the equations can only be solved for the case $M$ $=$ $2$ and subsequently an analytic expression is then derived. This contrasting behaviour between the $M$ $=$ $2$ and $M$ $>$ $2$ cases, which appears first at $O(1/N^2)$, is related to the fact that the anomalous dimensions of the bosonic fields are only equivalent for $M$ $=$ $2$.
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arxiv:hep-th/9307156
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We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum $E(k)$ or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter $q$ appears explictly in the one point functions in the theory, which can also be tested.
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arxiv:hep-th/9307180
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It is by now clear that the naive rule for the entropy of a black hole, {entropy} = 1/4 {area of event horizon}, is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, a rather different proof of this result is presented --- a proof based on Euclidean signature techniques. The total entropy is S = 1/4 {k A_H / l_P^2} + \int_H {S} \sqrt{g} d^2x. The integration runs over a spacelike cross-section of the event horizon H. The surface entropy density, {S}, is related to the behaviour of the matter Lagrangian under time dilations. Secondly, I shall consider the specific case of Einstein-Hilbert gravity coupled to an effective Lagrangian that is an arbitrary function of the Riemann tensor (though not of its derivatives). In this case a more explicit result is obtained S = 1/4 {k A_H / l_P^2} + 4 pi {k/hbar} \int_H {partial L / partial R_{\mu\nu\lambda\rho}} g^\perp_{\mu\lambda} g^\perp_{\nu\rho} \sqrt{g} d^2x . The symbol $g^\perp_{\mu\nu}$ denotes the projection onto the two-dimensional subspace orthogonal to the event horizon.
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arxiv:hep-th/9307194
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The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient $ {\bf R}^{2r}/W_A, $ $ r $ a rank of the gauge group, $ W_A $ the affine Weyl group. The PI formula resulting from Dirac's operator method contains a symmetrization with respect to $ W_A $ rather than the integration domain reduction. It gives a natural solution to Gribov's problem. Some features of fermion quantum dynamics caused by the nontrivial phase space geometry are briefly discussed.
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arxiv:hep-th/9308002
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The complete structure of the moduli space of \cys\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.
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arxiv:hep-th/9308005
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We generalize to composite operators concepts and techniques which have been successful in proving renormalization of the effective Action in light-cone gauge. Gauge invariant operators can be grouped into classes, closed under renormalization, which is matrix-wise. In spite of the presence of non-local counterterms, an ``effective" dimensional hierarchy still guarantees that any class is endowed with a finite number of elements. The main result we find is that gauge invariant operators under renormalization mix only among themselves, thanks to the very simple structure of Lee-Ward identities in this gauge, contrary to their behaviour in covariant gauges.
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arxiv:hep-th/9308006
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This is the second in a series of papers devoted to open string field theory in two dimensions. In this paper we aim to clarify the origin and the role of discrete physical states in the theory. To this end, we study interactions of discrete states and generic tachyons. In particular, we discuss at length four point amplitudes. We show that behavior of the correlation functions is governed by the number of generic tachyons involved and values of the kinematic invariants $s$, $t$ and $u$. Divergence of certain classes of correlators is shown to be the consequence of the fact certain kinematic invariants are non--positive integers in that case. Explicit examples are included. We check our results by standard conformal technique.
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arxiv:hep-th/9308050
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In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed by Callan, Giddings, Harvey and Strominger. The crucial observation is that the conformal anomaly can be cohomologically trivial and so not truly anomalous in such dilaton gravity models.
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arxiv:hep-th/9308095
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We analyze the Gribov problem for $\SU(N)$ and $\U(N)$ Yang-Mills fields on $d$-dimensional tori, $d=2,3,\ldots$. We give an improved version of the axial gauge condition and find an infinite, discrete group $\cG'=\Z^{dr}\rtimes({\Z_2}^{N-1}\rtimes\Z_2)$, where $r=N-1$ for $\GG=\SU(N)$ and $r=N$ for $\GG=\U(N)$, containing all gauge transformations compatible with that condition. This residual gauge group $\cG'$ provides (generically) all Gribov copies and allows to explicitly determine the space of gauge orbits which is an orbifold. Our results apply to Yang-Mills gauge theories either in the Lagrangian approach on $d$-dimensional space-time $T^d$, or in the Hamiltonian approach on $(d+1)$-dimensional space-time $T^d\times \R$. Using the latter, we argue that our results imply a non-trivial structure of all physical states in any Yang-Mills theory, especially if also matter fields are present.
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arxiv:hep-th/9308115
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Two local macros are included (gothic.sty and fleqn.sty)
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arxiv:hep-th/9308132
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Consistency of quantum mechanics in black hole physics requires unusual Lorentz transformation properties of the size and shape of physical systems with momentum beyond the Planck scale. A simple parton model illustrates the kind of behavior which is needed. It is then shown that conventional fundamental string theory shares these features.
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arxiv:hep-th/9308139
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The structure of physical operators and states of the unified constraint dynamics is studied. The genuine second--class constraints encoded are shown to be the superselection operators. The unified constrained dynamics is established to be physically--equivalent to the standard BFV--formalism with constraints split.
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arxiv:hep-th/9308140
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In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras can be viewed as reductions of affine Lie algebras. The hierarchies of integrable evolution equations associated to these classical W algebras are constructed as well as the generalized Toda field theories which have them as Noether symmetry algebras. The problem of quantising the DS reductions is solved for arbitrary $sl_2$ embeddings and it is shown that any W algebra can be embedded into an affine Lie algebra. This also provides us with an algorithmic method to write down free field realizations for arbitrary W algebras. Just like affine Lie algebras W algebras have finite underlying structures called `finite W algebras'. We study the classical and quantum theory of these algebras, which play an important role in the theory of ordinary W algebras, in detail as well as some aspects of their representation theory. The symplectic leaves (or W-coadjoint orbits) associated to arbitrary finite W algebras are determined as well as their realization in terms of bosoic oscillators. Apart from these technical aspects we also review the potential applications of W symmetry to string theory, 2-dimensional critical phenomena, the quantum Hall effect and solitary wave phenomena. This work is based on the Ph.D. thesis of the author.
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arxiv:hep-th/9308146
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It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be {\em explicitely} canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non--trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the {\em same} finite dimensional quantum mechanical system.
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arxiv:hep-th/9308155
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Consideration of the model of the relativistic particle with curvature and torsion in the three-dimensional space-time shows that the squaring of the primary constraints entails a wrong result. The complete set of the Hamiltonian constraints arising here correspond to another model with an action similar but not identical with the initial action.
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arxiv:hep-th/9309021
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Dynamics of cylindrical and spherical relativistic domain walls is investigated with the help of a new method based on Taylor expansion of the scalar field in a vicinity of the core of the wall. Internal oscillatory modes for the domain walls are found. These modes are non-analytic in the "width" of the domain wall. Rather non-trivial transformation to a special coordinate system, widely used in investigations of relativistic domain walls, is studied in detail.
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arxiv:hep-th/9309089
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The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the minimal table are identified with the gravitational descendants. Using the discrete states of ghost number zero and one we construct the currents and investigate the Ward identities which are identified with the W and the Virasoro constraints. As nontrivial examples we derive the $L_0$, $L_1$ and $W_{-1}^{(3)}$ equations exactly. $L_n$ and $W^{(k)}_n$ equations are also discussed. We then explicitly show the decoupling of the edge states $O_j ~(j=0~ {\rm mod}~ q) $. We consider the interaction theory perturbed by the cosmological constant $O_1$ and the screening charge $S^+ =O_{2q+1}$. The formalism can be easily generalized to potential models other than the screening charge.
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arxiv:hep-th/9309094
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We show that integrable vertex and RSOS models with trigonometric Boltzmann weights and appropriate inhomogeneities provide a convenient lattice regularization for massive field theories and for the recently studied massless field theories that interpolate between two non trivial conformal field theories. Massive and massless S matrices are computed from the lattice Bethe ansatz.
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arxiv:hep-th/9309135
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Series for the Wilson functions of an ``environmentally friendly'' renormalization group are computed to two loops, for an $O(N)$ vector model, in terms of the ``floating coupling'', and resummed by the Pad\'e method to yield crossover exponents for finite size and quantum systems. The resulting effective exponents obey all scaling laws, including hyperscaling in terms of an effective dimensionality, ${d\ef}=4-\gl$, which represents the crossover in the leading irrelevant operator, and are in excellent agreement with known results.
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arxiv:hep-th/9310086
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Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential $$V(r,\theta,\phi)={\omega^2\over 4}r^2 + {\delta\over r^2}+{C\over r^2 sin^2\theta}+{D\over r^2 cos^2\theta} + {F\over r^2 sin^2\theta sin^2 \alpha\phi} +{G\over r^2 sin^2\theta cos^2\alpha\phi}$$ with 7 parameters.Other algebraically solvable examples are also given.
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arxiv:hep-th/9310104
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We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $ sl(2) $-Yangians. This $ Y(sl(2)) \oplus Y(sl(2)) $ symmetry is an extension of the well-known $ sl(2) \oplus sl(2) $ . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.
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arxiv:hep-th/9310158
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The concept of ``elements of reality" is analyzed within the framework of quantum theory. It is shown that elements of reality fail to fulfill the product rule. This is the core of recent proofs of the impossibility of a Lorentz-invariant interpretation of quantum mechanics. A generalization and extension of the concept of elements of reality is presented. Lorentz-invariance is restored by giving up the product rule. The consequences of giving up the ``and" rule, which must be abandoned together with the product rule, are discussed.
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arxiv:hep-th/9310176
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Associated with the fundamental representation of a quantum algebra such as $U_q(A_1)$ or $U_q(A_2)$, there exist infinitely many gauge-equivalent $R$-matrices with different spectral-parameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the $R$-matrices in different gradations. Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
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arxiv:hep-th/9310183
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In the Higgs phase we may be left with a residual finite symmetry group H of the condensate. The topological interactions between the magnetic- and electric excitations in these so-called discrete H gauge theories are completely described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle H. Consequently, the finite number of physically inequivalent discrete H gauge theories obtained in this way are labelled by the elements of the cohomology group H^3(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at `The III International Conference on Mathematical Physics, String Theory and Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor. Math. Phys.)
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arxiv:hep-th/9311162
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In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom ($S=-\beta\cos\theta$). We find that the failure is not due to the defect of complex Langevin simulation itself, but rather to the way how one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the ${1/\beta}$ behaviour of the expectation value $<\cos\theta>$ in the small $\beta$ limit.
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arxiv:hep-th/9311174
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In two dimensions large N QCD with quarks, defined on the plane, is equivalent to a modified string theory with quarks at the ends and taken in the zero fold sector. The equivalence that was established in 1975 was expressed in the form of an interacting string action that reproduces the spectrum and the 1/N interactions of 2D QCD. This action may be a starting point for an analytic continuation to a four dimensional string version of QCD. After reviewing the old work I discuss relations to recent developments in the pure QCD-string equivalence on more complicated background %geometries.
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arxiv:hep-th/9312018
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The quantum symmetry of a rational quantum field theory is a finite- dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided monoidal C^*-category. Various properties of such algebraic structures are described, and some ideas concerning the classification programme are outlined. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Teor.Mat.Fiz.)
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arxiv:hep-th/9312026
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We review nonlinear gauge theory and its application to two-dimensional gravity. We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincar{\' e} algebra, which is the new Yang-Mills like formulation of the gravitational theory. As typical examples, we investigate $R^2$ gravity with dynamical torsion and generic form of 'dilaton' gravity. The supersymmetric extension of this theory is also discussed.
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arxiv:hep-th/9312059
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The generalised quasienergy states are introduced as eigenstates of the new integral of motion for periodically and nonperiodically kicked quantum systems.The photon distribution function of polymode generalised correlated light expressed in terms of multivariable Hermite polynomials is discussed and the relation of its properties to Schrodinger uncertainty relation is given.
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arxiv:hep-th/9312061
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We present a simple renormalizable abelian gauge model which includes antisymmetric second-rank tensor fields as matter fields rather than gauge fields known for a long time. The free action is conformally rather than gauge invariant. The quantization of the free fields is analyzed and the one-loop renormalization-group functions are evaluated. Transverse free waves are found to convey no energy. The coupling constant of the axial-vector abelian gauge interaction exhibits asymptotically free ultraviolet behavior, while the self-couplings of the tensor fields do not asymptotically diminish.
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arxiv:hep-th/9312062
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This is a review on infinite non-abelian symmetries in two-dimensional field theories. We show how any integrable QFT enjoys the existence of infinitely many {\bf conserved} charges. These charges {\bf do not commute} between them and satisfy a Yang--Baxter algebra. They are generated by quantum monodromy operators and provide a representation of $q-$deformed affine Lie algebras $U_q({\hat\G})$. We review the work by de Vega, Eichenherr and Maillet on the bootstrap construction of the quantum monodromy operators in classically scale invariant theories where the classical monodromy matrix is conserved. Then, the recent generalization to the sine--Gordon (or massive Thirring) model, where such operators do not possess a classical analogue is given (This provides a representation of $S{\hat U}(2)_q$). It is then reported on the recent work by Destri and de Vega, where both commuting and non-commuting integrals of motion are systematically obtained by Bethe Ansatz in the light-cone approach. The eigenvalues of the six--vertex alternating transfer matrix $\tau(\l)$ are explicitly computed on a generic physical state through algebraic Bethe ansatz. In the thermodynamic limit $\tau(\l)$ turns out to be a two--valued periodic function. One determination generates the local abelian charges, including energy and momentum, while the other yields the abelian subalgebra of the (non--local) YB algebra. In particular, the bootstrap results coincide with the ratio between the two determinations of the lattice transfer matrix.[Based on a Lecture at the Clausthal Symposium].
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arxiv:hep-th/9312084
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$D=2$ free string in linear dilaton background is considered in so called target space/world-sheet light cone gauge $ X^{+}=0,~g_{++}=0,~g_{+-}=1$. After gauge fixing the theory has the residual Virasoro and $U(1)$ current symmetries. The physical spectrum related to $SL_2$ invariant vacuum is found to be trivial. We find that the theory has a nontrivial spectrum if the states in different non-equivalent representations ("pictures") of CFT algebra of matter fields are considered.
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arxiv:hep-th/9312120
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The first three coefficients in an expansion of the heat kernel of a nonminimal nonabelian kinetic operator taken in an arbitrary background gauge in arbitrary space-time dimension are calculated
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arxiv:hep-th/9312138
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The analogue of the Poisson bracket for the De Donder-Weyl (DW) Hamiltonian formulation of field theory is proposed. We start from the Hamilton- Poincar\'{e}-Cartan (HPC) form of the multidimensional variational calculus and define the bracket on the differential forms over the space-time (=horizontal forms). This bracket is related to the Schouten-Nijenhuis bracket of the multivector fields which are associated with the horizontal forms by means of the "polysymplectic form". The latter is given by the HPC form and generalizes the symplectic form to field theory. We point out that the algebra of forms with respect to our Poisson bracket and the exterior product has the structure of the Gerstenhaber graded algebra. It is shown that the Poisson bracket with the DW Hamiltonian function generates the exterior differential thus leading to the bracket representation of the DW Hamiltonian field equations. Few illustrative examples are also presented.
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arxiv:hep-th/9312162
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We discuss a generalization of the quantum group $\su$ to the $q$-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a (1+1)-dimensional fermion. As an application of the quantum group symmetry, we discuss a model of quantum group current on the analogy of the Hall current.
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arxiv:hep-th/9312174
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We construct a cohomology theory controlling the deformations of a general Drinfel'd algebra. The picture presented here has two sides -- the combinatorial one related with the fact of the existence of a graded Lie algebra structure on the simplicial cochain complex of the associahedra, and the algebraic one related with the algebra of derivations on the bar construction.
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arxiv:hep-th/9312196
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In the spirit of classic works of Wilson on the renormalization group and operator product expansion, a new framework for the study of the theory space of euclidean quantum field theories has been introduced. This formalism is particularly useful for elucidating the structure of the short-distance expansions of the $n$-point functions of a renormalizable quantum field theory near a non-trivial fixed point. We review and apply this formalism in the study of the scaling limit of the two dimensional massive Ising model. Renormalization group analysis and operator product expansions determine all the non-analytic mass dependence of the short-distance expansion of the correlation functions. An extension of the first order variational formula to higher orders provides a manifestly finite scheme for the perturbative calculation of the operator product coefficients to any order in parameters. A perturbative expansion of the correlation functions follows. We implement this scheme for a systematic study of correlation functions involving two spin operators. We show how the necessary non-trivial integrals can be calculated. As two concrete examples we explicitly calculate the short-distance expansion of the spin-spin correlation function to third order and the spin-spin-energy density correlation function to first order in the mass. We also discuss the applicability of our results to perturbations near other non-trivial fixed points corresponding to other unitary minimal models.
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arxiv:hep-th/9312207
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The geodesic motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space is analysed. The generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. A simple exact solution, corresponding to trajectories lying on a cone, is given.
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arxiv:hep-th/9401036
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We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of $M$ which is the relevant object for structureless particles. In particular, we compute these generalized braid groups for particles with an internal spin degree of freedom on an arbitrary $M$. A study of their unitary representations allows us to determine the available spectrum of spin and statistics on $M$ in a certain class of quantum theories. One interesting result is that half-integral spin quantizations are obtained on certain manifolds having an obstruction to an ordinary spin structure. We also compare our results to corresponding ones for topological solitons in $O(d+1)$-invariant nonlinear sigma models in $(d+1)$-dimensions, generalizing recent studies in two spatial dimensions. Finally, we prove that there exists a general scalar quantum theory yielding half-integral spin for particles (or $O(d+1)$ solitons) on a closed, orientable manifold $M$ if and only if $M$ possesses a ${\rm spin}_c$ structure.
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arxiv:hep-th/9401074
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We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of the parameter which characterizes the boundary conditions, the boundary starts receeding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, an asymptotic observer using normal time resolutions will always measure large fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly the quantum gravity effects.
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arxiv:hep-th/9401102
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We consider the forced harmonic oscillator quantized according to infinite statistics ( a special case of the `quon' algebra proposed by Greenberg ). We show that in order for the statistics to be consistently evolved the forcing term must be identically zero for all time. Hence only the free harmonic oscillator may be quantized according to infinite statistics.
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arxiv:hep-th/9401162
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We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson $q$-integral as indefinite integration on the braided group of functions in one variable $x$. Here $x$ is treated with braid statistics $q$ rather than the usual bosonic or Grassmann ones. We show that the definite integral $\int x$ can also be evaluated algebraically as multiples of the integral of a $q$-Gaussian, with $x$ remaining as a bosonic scaling variable associated with the $q$-deformation. Further composing our algebraic integration with a representation then leads to ordinary numbers for the integral. We also use our integration to develop a full theory of $q$-Fourier transformation $F$. We use the braided addition $\Delta x=x\otimes 1+1\otimes x$ and braided-antipode $S$ to define a convolution product, and prove a convolution theorem. We prove also that $F^2=S$. We prove the analogous results on any braided group, including integration and Fourier transformation on quantum planes associated to general R-matrices, including $q$-Euclidean and $q$-Minkowski spaces.
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arxiv:hep-th/9402037
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It is shown that the well known Racah sum rule and Biedenharn-Elliott identity satisfied by the recoupling coefficients or by the $6-j$ symbols of the usual rotation $SO(3)$ algebra can be extended to the corresponding features of the super-rotation $osp(1|2)$ superalgebra. The structure of the sum rules is completely similar in both cases, the only difference concerns the signs which are more involved in the super-rotation case.
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arxiv:hep-th/9402040
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We show how to derive exact boundary $S$ matrices for integrable quantum field theories in 1+1 dimensions using lattice regularization. We do this calculation explicitly for the sine-Gordon model with fixed boundary conditions using the Bethe ansatz for an XXZ-type spin chain in a boundary magnetic field. Our results agree with recent conjectures of Ghoshal and Zamolodchikov, and indicate that the only solutions to the Bethe equations which contribute to the scaling limit are the standard strings.
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arxiv:hep-th/9402045
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The complete classification of WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of $A_1$ and $A_2$ and level 1 of all simple algebras. Here, we address the classification problem for the nicest high rank semi-simple affine algebras: $(A_1^{(1)})^{\oplus_r}$. Among other things, we explicitly find all automorphism invariants, for all levels $k=(k_1,\ldots,k_r)$, and complete the classification for $A_1^{(1)}\oplus A_1^{(1)}$, for all levels $k_1,k_2$. We also solve the classification problem for $(A_1^{(1)})^{\oplus_r}$, for any levels $k_i$ with the property that for $i\ne j$ each $gcd(k_i+2,k_j+2)\leq 3$. In addition, we find some physical invariants which seem to be new. Together with some recent work by Stanev, the classification for all $(A^{(1)}_1)^{\oplus_r}_k$ could now be within sight.
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arxiv:hep-th/9402074
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We construct a new class of exact string solutions with a four dimensional target space metric of signature ($-,+,+,+$) by gauging the independent left and right nilpotent subgroups with `null' generators of WZNW models for rank 2 non-compact groups $G$. The `null' property of the generators (${\rm Tr }(N_n N_m)=0$) implies the consistency of the gauging and the absence of $\a'$-corrections to the semiclassical backgrounds obtained from the gauged WZNW models. In the case of the maximally non-compact groups ($G= SL(3), SO(2,2), SO(2,3), G_2$) the construction corresponds to gauging some of the subgroups generated by the nilpotent `step' operators in the Gauss decomposition. The rank 2 case is a particular example of a general construction leading to conformal backgrounds with one time-like direction. The conformal theories obtained by integrating out the gauge field can be considered as sigma model analogs of Toda models (their classical equations of motion are equivalent to Toda model equations). The procedure of `null gauging' applies also to other non-compact groups.
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arxiv:hep-th/9402120
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Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras in the superspace formalism. We show that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum hamiltonian reduction reduces to quantum hamiltonian reduction of non-supersymmetric Lie superalgebras. We construct explicitly the super energy-momentum tensor, as well as all generators of spin 1 (and $\hf$); thus we construct explicitly all generators in the superconformal, quasi-superconformal and $\Z_2 \times \Z_2$ superconformal algebras.
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arxiv:hep-th/9403012
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We apply various conventional tests of integrability to the supersymmetric nonlinear Schr\"odinger equation. We find that a matrix Lax pair exists and that the system has the Painlev\'e property only for a particular choice of the free parameters of the theory. We also show that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. We are unable to construct a zero curvature formulation of the equations based on OSp(2$|$1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schr\"odinger equation which appears to possess the Painlev\'e property.
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arxiv:hep-th/9403019
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We analyze quasi-topological solitons winding around a mexican-hat potential in two space-time dimensions. They are prototypes for a large number of physical excitations, including Skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagnetic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for classical stability, and show that contrary to the naive expectation these can be satisfied in the weak-coupling limit. In this limit we can calculate the soliton properties reliably, and estimate their lifetime semiclassically. We explain why gauge interactions destabilize these solitons, unless the scalar sector is extended.
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arxiv:hep-th/9403034
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Developing upon the ideas of ref. \ref{6}, it is shown how the theory of classical $W$ algebras can be formulated on a higher genus Riemann surface in the spirit of Krichever and Novikov. The basic geometric object is the Drinfeld--Sokolov principal bundle $L$ associated to a simple complex Lie group $G$ equipped with an $SL(2,\Bbb C)$ subgroup $S$, whose properties are studied in detail. On a multipunctured Riemann surface, the Drinfeld--Sokolov--Krichever--Novikov spaces are defined, as a generalization of the customary Krichever--Novikov spaces, their properties are analyzed and standard bases are written down. Finally, a WZWN chiral phase space based on the principal bundle $L$ with a KM type Poisson structure is introduced and, by the usual procedure of imposing first class constraints and gauge fixing, a classical $W$ algebra is produced. The compatibility of the construction with the global geometric data is highlighted.
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arxiv:hep-th/9403036
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This paper considers closed-string states of type 2b superstring theory in which the whole string is localized at a single point in superspace. Correlation functions of these (scalar and pseudoscalar) states possess an infinite number of position-space singularities inside and on the light-cone as well as a space-like singularity outside the light-cone.\foot{This paper was previously produced as preprint QMW-91-02.}
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arxiv:hep-th/9403040
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It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
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arxiv:hep-th/9403042
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We begin with a prior observation by one of us that Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a nonabelian Berry vector potential. We ask what object produces the nonabelian potential in parameter space, in the same sense that the abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole, (centered at the point where the level becomes degenerate with another), as shown by Berry. We find that it is a {\em meron}, an object in four euclidean dimensions with instanton number ${1 \over 2}$, centered at the point where the doubly degenerate positive and negative energy levels of the Dirac equation become fourfold degenerate.
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arxiv:hep-th/9403076
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In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the ``information problem'' in black hole physics
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arxiv:hep-th/9403108
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Invertible universal R-matrices of quantum Lie algebras do not exist at roots of unity. There exist however quotients for which intertwiners of tensor products of representations always exist, i.e. R-matrices exist in the representations. One of these quotients, which is finite dimensional, has a universal R-matrix. In this paper, we answer the following question: on which condition are the different quotients of U_q(sl(2)) (Hopf)-equivalent? In the case when they are equivalent, the universal R-matrix of one can be transformed into a universal R-matrix of the other. We prove that this happens only when q^4=1, and we explicitly give the expressions for the automorphisms and for the transformed universal R-matrices in this case.
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arxiv:hep-th/9403110
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Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the $q$--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}
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arxiv:hep-th/9403114
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