TBA equations for excited states in the O(3) and O(4) nonlinear $\sigma$-model

TL;DR

This paper develops TBA integral equations for excited states in the O(3) and O(4) nonlinear sigma models, enabling precise computation of the mass gap and comparison with perturbative and Monte Carlo results.

Contribution

It introduces TBA equations for excited states in the sigma models and computes the exact mass gap, extending previous ground state analyses.

Findings

Exact mass gap computed for O(3) and O(4) models

Results agree with 3-loop perturbation theory

Results validated against Monte Carlo data

Abstract

TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.