Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

TL;DR

This paper connects the representation theory of Yetter-Drinfeld modules over braided Hopf algebras with integrable perturbations in conformal field theories, revealing quantum groups governing symmetries.

Contribution

It introduces a method to identify quantum groups associated with integrable perturbations of conformal field theories using a construction similar to Lusztig's.

Findings

Quantum group for loop algebra of sl(2) appears in perturbed free boson models

Establishes a link between representation theory and integrable quantum field theories

Provides a new approach to determine symmetries in perturbed conformal field theories

Abstract

In this paper we relate a problem in representation theory - the study of Yetter-Drinfeld modules over certain braided Hopf algebras - to a problem in two-dimensional quantum field theory, namely the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.