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. 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, 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 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.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- June 1993
- DOI:
- 10.1016/0393-0440(93)90056-K
- arXiv:
- arXiv:hep-th/9209076
- Bibcode:
- 1993JGP....11..251F
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 28 pages, omitted % added, LATEX file, IHES/P/92/73