Off-critical $W_\infty$ and Virasoro Algebras As Dynamical Symmetries Of the Integrable Models

TL;DR

This paper uncovers an infinite set of new conserved charges in perturbed conformal field theories, forming a complex algebra of $W_$ and Virasoro symmetries that influence correlation function calculations.

Contribution

It introduces a criterion for the existence of these conserved charges and demonstrates their algebraic structure in specific integrable models.

Findings

New noncommuting conserved charges found in perturbed CFTs

The charges form two $W_$ algebras with Virasoro subalgebras

One Virasoro algebra is crucial for computing correlation functions

Abstract

We find an infinite set of new noncommuting conserved charges in a specific class of perturbed CFT's and present a criterion for their existence.They appear to be higher momenta of the already known commuting conserved currents.The algebra they close consists of two noncommuting$W_\infty$ algebras.We find various Virasoro subalgebras of the full symmetry algebra. It is shown on the examples of the perturbed Ising and Potts models that one of them plays an essencial role in the computation of the correlation functions of the fields of the theory.