Deformed Minimal Models and Generalized Toda Theory

TL;DR

This paper introduces a generalized Toda theory based on non-abelian groups, deriving integrable deformations of minimal conformal models like the critical Ising model, with explicit conserved charges and soliton solutions.

Contribution

It extends Toda theory to non-abelian groups and constructs integrable deformations of minimal models using gauged Wess-Zumino-Witten actions.

Findings

Derived infinite conserved charges for deformed models

Constructed soliton solutions from Lax pairs

Connected deformations to specific minimal model operators

Abstract

We introduce a generalization of $A_{r}$-type Toda theory based on a non-abelian group G, which we call the $(A_{r},G)$-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine $(A_{1},SU(2))$-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator $\Phi_{(2,1)}$. We derive infinite conserved charges and soliton solutions from the Lax pair of the affine $(A_{1}, SU(2))$-Toda theory. Another type of integrable deformation which accounts for the $\Phi_{(3,1)}$-deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.