LATTICE CONFORMAL THEORIES AND THEIR INTEGRABLE PERTURBATIONS

TL;DR

This paper develops lattice analogues of conformal theories like WZW and Toda models, introducing discrete reductions, perturbation theory, and linking these models to integrable hierarchies such as KP.

Contribution

It presents novel lattice formulations of conformal theories, including discrete reductions and connections to integrable hierarchies, expanding the understanding of lattice conformal models.

Findings

Discrete Drinfeld-Sokolov reduction for lattice WZW models

Formulation of perturbation theory in the chiral sector

Identification of the lattice WZW model within the KP hierarchy

Abstract

We consider lattice analogues of some conformal theories, including WZW and Toda models. We describe discrete versions of Drinfeld-Sokolov reduction and Sugawara construction for the WZW model. We formulate perturbation theory in chiral sector. We describe the spaces of Integrals of Motion in the perturbed theories. We interpret the perturbed WZW model in terms of NLS hierarchy and obtain of this model into the lattice KP-hierarchy.