On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model

TL;DR

This paper investigates the analytic and numerical properties of the thermodynamic Bethe ansatz equation in the sinh-Gordon model, exploring its complex structure and potential links to conformal field theory and massless models.

Contribution

It provides new insights into the analytic structure of the sinh-Gordon TBA solution and suggests connections to CFT integrable structures and massless models.

Findings

Identification of implicit periodic structures in the TBA solution

Analysis of the complex analytic structure of the solution

Hints at relevance of CFT structures in sinh-Gordon and related models

Abstract

Two implicit periodic structures in the solution of sinh-Gordon thermodynamic Bethe ansatz equation are considered. The analytic structure of the solution as a function of complex $\theta$ is studied to some extent both analytically and numerically. The results make a hint how the CFT integrable structures can be relevant in the sinh-Gordon and staircase models. More motivations are figured out for subsequent studies of the massless sinh-Gordon (i.e. Liouville) TBA equation.