pith. sign in

arxiv: hep-th/9209076 · v2 · submitted 1992-09-22 · ✦ hep-th

Lattice Wess-Zumino-Witten Model and Quantum Groups

classification ✦ hep-th
keywords quantumlatticemodelsymmetrytheoryalgebrachiralcurrent
0
0 comments X
read the original abstract

Quantum groups play a 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. We discuss specifically the Wess-Zumino-Witten conformally invariant quantum field model combining two chiral parts which describe the left- and right-moving degrees of freedom. On one hand side, the quantum group plays the role of the symmetry of the chiral components of the theory. On the other hand, the model admits a lattice regularization (in the Minkowski space) in which the current algebra symmetry of the theory also becomes quantum, providing the simplest example of a quantum group symmetry coupling space-time and internal degrees of freedom. We develop a free field approach to the representation theory of the lattice $sl(2)$-based current algebra and show how to use it to rigorously construct an exact solution of the quantum $SL(2)$ WZW model on lattice.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes

    hep-th 2025-05 unverdicted novelty 6.0

    Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entr...