The dilute A_L models and the integrable perturbations of unitary minimal CFTs

TL;DR

This paper connects lattice models known as dilute A_L models with the thermodynamic Bethe ansatz equations for perturbed minimal conformal field theories, confirming conjectures through explicit scaling limits.

Contribution

It demonstrates how the TBA equations for perturbed minimal models can be derived from dilute A_L lattice models in specific regimes.

Findings

TBA equations are recovered from dilute A_L models in the scaling limit.

Explicit examples M_{5,6}+_{1,2} and M_{3,4}+_{2,1} confirm the conjecture.

Lattice models provide a concrete realization of the continuum TBA results.

Abstract

Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by \phi_{1,2} or \phi_{2,1} operator. We examine their results in view of the lattice analogues, dilute A_L models at regime 1 and 2. Taking M_{5,6}+\phi_{1,2} and M_{3,4}+\phi_{2,1} as the simplest examples, we will explicitly show that the conjectured TBA equations can be recovered from the lattice model in a scaling limit.