A Two-loop Test of Buscher's T-duality I

TL;DR

This paper verifies the quantum equivalence of sigma models related by Buscher's T-duality at two loops, confirming their free energy densities match in a specific deformed SU(2) model.

Contribution

It provides a detailed two-loop calculation demonstrating the quantum equivalence of T-dual sigma models, extending previous one-loop results.

Findings

Two-loop free energy densities agree for T-dual models

Dimensional regularization used in perturbative calculations

Supports quantum equivalence of T-dual sigma models

Abstract

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.