TBA equations for the mass gap in the O(2r) non-linear sigma-models

TL;DR

This paper introduces TBA integral equations for 1-particle states in the O(n) non-linear sigma-models with even n, derived from analytic properties and Luscher's formula, and confirms their accuracy through numerical comparison with perturbation theory.

Contribution

The paper proposes new TBA equations for the O(2r) sigma-models based on analytic properties and Luscher's formula, extending the understanding of mass gaps in these models.

Findings

Numerical solutions of TBA equations match three-loop perturbation results for small volumes.

The proposed TBA system is consistent with known asymptotic behaviors.

The approach provides a new way to analyze mass gaps in non-linear sigma-models.

Abstract

We propose TBA integral equations for 1-particle states in the O(n) non-linear sigma-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system.