Y-System and Deformed Thermodynamic Bethe Ansatz

TL;DR

This paper introduces the Deformed Thermodynamic Bethe Ansatz, a new analytical tool for studying the monodromy problem of the cubic oscillator, generalizing previous methods and connecting to known models like the 3-state Potts model.

Contribution

It presents the Deformed TBA system of coupled nonlinear integral equations and the associated Y-system with a geometric interpretation, extending prior analyses.

Findings

Deformed TBA reduces to Zamolodchikov TBA in special cases

Y-system has an elegant geometric interpretation

Method generalizes Dorey-Tateo analysis

Abstract

We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe Ansatz), to analyze the monodromy problem of the cubic oscillator. The Deformed TBA is a system of five coupled nonlinear integral equations, which in a particular case reduces to the Zamolodchikov TBA equation for the 3-state Potts model. Our method generalizes the Dorey-Tateo analysis of the (monomial) cubic oscillator. We introduce a Y-system corresponding to the Deformed TBA and give it an elegant geometric interpretation.