The thermodynamic Bethe ansatz for deformed W$A_{N-1}$ conformal field theories

TL;DR

This paper develops thermodynamic Bethe ansatz equations for deformed W$_{N-1}$ conformal field theories, capturing their flow between fixed points and matching expected ultraviolet and infrared behaviors.

Contribution

It introduces a novel set of TBA equations for minimal $W_p^N$ models perturbed by a specific primary field, extending understanding of their RG flows.

Findings

Equations reproduce ultraviolet and infrared regimes accurately.

Describe the ground state flow from $W_p^N$ to $W_{p-1}^N$ fixed point.

Match expected theoretical behaviors in perturbed conformal field theories.

Abstract

We propose and investigate the thermodynamic Bethe ansatz equations for the minimal $W_p^N$ models~(associated with the $A_{N-1}$ Lie algebra) perturbed by the least~($Z_N$ invariant) primary field $\Phi_N$. Our results reproduce the expected ultraviolet and infrared regimes. In particular for the positive sign of the perturbation our equations describe the behaviour of the ground state flowing from the $W_p^N$ model to the next $W_{p-1}^N$ fixed point.