# 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…

## 9 Citations

Regular Basis and R-Matrices for the ^(su)(n)k Knizhnik–Zamolodchikov Equation

- Physics, Mathematics
- 2000

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. They…

Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model

- Physics
- 2017

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 a…

Canonical approach to the WZNW model

- Physics, Mathematics
- 2014

The chiral Wess-Zumino-Novikov-Witten (WZNW) model provides the simplest class of rational conformal field theories which exhibit a non-abelian braid-group statistics and an associated "quantum…

Chiral zero modes of the SU(n) WZNW model

- Physics
- 2002

We define the chiral zero modes’ phase space of the G = SU(n) Wess-Zumino-Novikov-Witten (WZNW) model as an (n − 1)(n + 2)dimensional manifold Mq equipped with a symplectic form Ωq involving a…

Quantum matrix algebra for the SU(n) WZNW model

- Mathematics, Physics
- 2003

The zero modes of the chiral SU (n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a = (a i α ), i, α = 1,....,n (with noncommuting entries) and by…

Chiral zero modes of the SU(n) Wess–Zumino–Novikov–Witten model

- Mathematics, Physics
- 2003

We define the chiral zero modes' phase space of the G = SU(n) Wess–Zumino–Novikov–Witten (WZNW) model as an (n − 1)(n + 2)-dimensional manifold q equipped with a symplectic form Ωq involving a…

Generalized Grassmann algebras and its connection to the extended supersymmetric models

- Physics
- 2001

It is shown that the fermionic Heisenberg-Weyl algebra with 2N=D fermionic generators is equivalent to the generalized Grassmann algebra with two fractional generators. The 2,3 and 4 dimensional…

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

- Mathematics, Physics
- 2007

A zero modes’ Fock space $$\mathcal{F}_{q}$$ is constructed for the extended chiral $${su(2)}$$ WZNW model. It gives room to a realization of the fusion ring of representations of the restricted…

Institute for Mathematical Physics

- 2000

Collection of Abstracts of the Lectures which will be given at the International Workshop \Mathematical Physics { today, Priority Technologies { for tomorrow"

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