Corpus ID: 15683286

A Finite Dimensional Gauge Problem in the WZNW Model

@article{DuboisViolette1999AFD,
  title={A Finite Dimensional Gauge Problem in the WZNW Model},
  author={Michel Dubois-Violette and Paolo Furlan and Ludmil K. Hadjiivanov and A. P. Isaev and Pavel Pyatov and Ivan Todorov Todorov},
  journal={arXiv: High Energy Physics - Theory},
  year={1999}
}
The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each of these matrix algebras admits an ideal such that the corresponding factor algebra is finite dimensional. The structure of superselection sectors of the (diagonal) 2D WZNW model is then reduced to a finite dimensional problem of a gauge theory type. For n=2… Expand
Regular Basis and R-Matrices for the ^(su)(n)k Knizhnik–Zamolodchikov Equation
Dynamical R-matrix relations are derived for the group-valued chiral vertex operators in the SU(n) WZNW model from the KZ equation for a general four-point function including two step operators. TheyExpand
Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model
Wess–Zumino–Novikov–Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2D) rational conformal field theories (RCFTs). A WZNW chiral state space is aExpand
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References

SHOWING 1-10 OF 119 REFERENCES
A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model
The cannonical quantization of the WZNW model provides a complete set of exchange relation in the enlarged chiral state spaces that include the Gauss components M±, of the monodromy matrices M, .Expand
Generalized Homologies for the Zero Modes of the SU(2) WZNW Model
We generalize the BRS method for the (finite-dimensional) quantum gauge theory involved in the zero modes of the monodromy extended SU(2) WZNW model. The generalization consists of a nilpotentExpand
Canonical approach to the quantum WZNW model
The canonical approach to the chiral SU(n) WZNW model with a monodromy independent r{matrix is reviewed. Taking the quantum group symmetry of the model (which re ects its classical Poisson{LieExpand
Operator realization of the SU(2) WZNW model
Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables M and M. Earlier work on the subject,Expand
Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory - Nucl. Phys. B241, 333 (1984)
We present an investigation of the massless, two-dimentional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic)Expand
Current algebra approach to conformal invariant two-dimensional models
Abstract A critical chiral QFT in 1 + 1 dimensions is determined by conformal and internal symmetry properties of the basic fields. The free parameters multiplying the Schwinger terms in the currentExpand
Lattice Wess-Zumino-Witten model and quantum groups
Abstract Quantum groups play the role of symmetries of integrable theories in two dimensions. They may be detected on the classical level as Poisson-Lie symmetries of the corresponding phase spaces.Expand
Hidden quantum groups inside Kac-Moody algebra
A lattice analogue of the Kac-Moody algebra is constructed. It is shown that the generators of the quantum algebra with the deformation parameterq=exp(iπ/k+h) can be constructed in terms ofExpand
Representation Theory of Lattice Current Algebras
Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantumExpand
Current Algebra and Wess-Zumino Model in Two-Dimensions
We investigate quantum field theory in two dimensions invariant with respect to conformal (Virasoro) and non-abelian current (Kac-Moody) algebras. The Wess-Zumino model is related to the special caseExpand
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