A new class of integrable deformations of CFTs

TL;DR

This paper introduces a new class of integrable sigma-models derived from current algebra theories on semisimple groups, revealing non-perturbative symmetries and demonstrating integrability through Hamiltonian analysis, extending to coset spaces.

Contribution

It presents a novel construction of integrable deformations of conformal field theories using asymmetric gauging, distinct from previous lambda-deformations, and demonstrates their integrability.

Findings

Constructed new integrable sigma-models for semisimple groups.

Discovered non-perturbative symmetries in coupling space.

Proved integrability in several specific cases.

Abstract

We construct a new class of integrable $\sigma$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for $G$ both at level $k$, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of $G/H$ CFTs and show integrability when $G/H$ is a symmetric space. Our method resembles that used for constructing the $\lambda$-deformed integrable $\sigma$-models, but the results are distinct and novel.