Thermodynamic Bethe Ansatz for G_k x G_l / G_{k+l} Coset Models Perturbed by Their \phi_{1,1,Adj} Operator

TL;DR

This paper develops a Thermodynamic Bethe Ansatz framework for specific G_k x G_l / G_{k+l} coset models perturbed by a particular operator, connecting to known models in certain limits and confirming expected central charge values.

Contribution

It introduces a novel TBA approach for G_k x G_l / G_{k+l} coset models perturbed by _{1,1,Adj}, revealing an adjacency structure and linking to WZW and Principal Chiral models in special limits.

Findings

UV and IR limits match expected central charges

Recovers TBA for G_l WZW model with perturbation

Derives TBA for Principal Chiral model with WZ term at large levels

Abstract

We propose a Thermodynamic Bethe Ansatz (TBA) for G_k x G_l / G_{k+l} conformal coset models (G any simply-laced Lie algebra) perturbed by their operator \phi_{1,1,Adj}. An interesting adjacency structure appears and can be depicted in a sort of ``product'' of Dynkin diagrams of G and A_{k+l-1}. UV and IR limits are computed and reproduce the expected values for the central charges. For k->\infty, l fixed we obtain the TBA of the G_l WZW model perturbed by J_a\bar{J}_a, and for k,l->\infty, k-l fixed, that of Principal Chiral model with WZ term at level k-l.