Integrable Perturbations of $W_n$ and WZW Models

TL;DR

This paper introduces a new class of 2D integrable models derived from perturbing minimal conformal field theories with W-symmetry, connecting them to WZW models and quantum group structures.

Contribution

It generalizes known perturbed Virasoro models to include W-symmetry and explores their algebraic structure and scattering behavior in the large minimal model limit.

Findings

Conserved charge algebra is noncommutative and matches twisted affine algebra G.

Models reduce to scalar perturbations of WZW theories at large p.

Scattering matrices are conjectured to relate to q-deformed G algebra at roots of unity.

Abstract

We present a new class of 2d integrable models obtained as perturbations of minimal CFT with W-symmetry by fundamental weight primaries. These models are generalisations of well known $(1,2)$-perturbed Virasoro minimal models. In the large $p$ (number of minimal model) limit they coincide with scalar perturbations of WZW theories. The algebra of conserved charges is discussed in this limit. We prove that it is noncommutative and coincides with twisted affine algebra $G$ represented in a space of asymptotic states. We conjecture that scattering in these models for generic $p$ is described by $S$-matrix of the $q$-deformed $G$ - algebra with $q$ being root of unity.