Elementary functions in Thermodynamic Bethe Ansatz

TL;DR

This paper finds explicit solutions to Thermodynamic Bethe Ansatz equations for various super-potentials using elementary functions, expanding on previous work in supersymmetric theories.

Contribution

It introduces a method to solve TBA equations for a broader class of super-potentials with elementary functions, building on the ODE/IM correspondence.

Findings

Solutions expressed in terms of modified Bessel functions.

Solutions expressed in terms of confluent hyper-geometric series.

Extended the class of super-potentials with explicit TBA solutions.

Abstract

Some years ago, Fendley found an explicit solution to Thermodynamic Bethe Ansatz (TBA) equation for a N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek for explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series.