Winding vacuum energies in a deformed O(4) sigma model

TL;DR

This paper develops a novel method to compute winding vacuum energies in a deformed O(4) sigma model by linking classical and quantum integrable systems, overcoming limitations of traditional techniques.

Contribution

It introduces a new approach to calculate winding energies using classical sinh-Gordon solutions, extending integrable quantum field theory methods.

Findings

Expressed winding energies via classical sinh-Gordon solutions

Overcame limitations of thermodynamic Bethe ansatz and non-linear integral equations

Provided a new computational framework for deformed sigma models

Abstract

We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.