TBA equations for excited states in the Sine-Gordon model

TL;DR

This paper develops TBA integral equations for excited states in the Sine-Gordon model, based on Bethe Ansatz, T- and Y-systems, and explores their properties and relations to other formulations.

Contribution

It introduces TBA equations for multiparticle states in the Sine-Gordon model derived from T- and Y-systems, unifying charge sectors and connecting to the Destri-deVega equation.

Findings

Explicit large volume solutions for Y-system functions

Unified treatment of even and odd charge sectors

Relation established between TBA Y-functions and Destri-deVega variables

Abstract

We propose TBA integral equations for multiparticle soliton (fermion) states in the Sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe Ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given.