Off critical current algebras

TL;DR

This paper explores the structure of infinite-dimensional algebras arising in integrable perturbations of conformal theories, extending known algebraic frameworks to non-abelian groups and analyzing their implications for symmetry and correlation functions.

Contribution

It introduces a non-abelian generalization of $W_$ algebras in integrable perturbations and studies their structure, including subalgebras and symmetry constraints.

Findings

Pure sectors coincide with conformal case

Identifies subalgebras as Kac-Moody algebras

Symmetry constraints determine correlation functions

Abstract

We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$ to the case of a non abelian group. We prove that the pure left-symmetry as well as the pure right-sector of the thus obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to be unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong, and in the case of the massive deformation of a non-abelian fermionic model, the symmetry alone is enough to fix the 2- and 3-point functions of the theory.