From A_m Trigonometric S-Matrices to the Thermodynamic Bethe Ansatz

TL;DR

This paper derives thermodynamic Bethe Ansatz equations for certain integrable models directly from trigonometric S-matrices associated with algebraic structures, clarifying their foundational connection.

Contribution

It explicitly connects the thermodynamic Bethe Ansatz equations to trigonometric S-matrices for algebraic models, providing a direct derivation method.

Findings

Derivation of TBA equations from trigonometric S-matrices.

Clarification of the link between algebraic S-matrices and integrable deformations.

Application to massive integrable deformations of coset conformal field theories.

Abstract

The thermodynamic Bethe Ansatz equations that have been proposed to describe massive integrable deformations of the coset conformal field theories $g_k\times g_l/g_{k+l}$ are shown to result directly by applying the usual thermodynamic Bethe Ansatz arguments to the trigonometric $S$-matrices for the algebras $g=a_{m-1}$.