Thermodynamical Bethe Ansatz analysis in an SU(2)xU(1) symmetric sigma-model

TL;DR

This paper compares thermodynamical Bethe Ansatz and perturbation theory calculations of free energies in an integrable SU(2)xU(1) sigma-model, confirming the S matrix and computing the mass gap.

Contribution

It provides a detailed analysis of free energies using TBA and perturbation theory in an SU(2)xU(1) symmetric sigma-model, validating the S matrix and calculating the mass gap.

Findings

Perfect agreement between TBA and perturbative results.

Confirmation of the proposed S matrix correctness.

Mass gap computed in multiple regularization schemes.

Abstract

Four different types of free energies are computed by both thermodynamical Bethe Ansatz (TBA) techniques and by weak coupling perturbation theory in an integrable one-parameter deformation of the O(4) principal chiral sigma-model (with SU(2)xU(1) symmetry). The model exhibits both `fermionic' and `bosonic' type free energies and in all cases the perturbative and the TBA results are in perfect agreement, strongly supporting the correctness of the proposed S matrix. The mass gap is also computed in terms of the Lambda parameters of the modified minimal substraction scheme and a lattice regularized version of the model.