On Quantum T-duality in sigma models

TL;DR

This paper investigates quantum equivalence of sigma models related by Abelian and non-Abelian T-duality using perturbation theory, deriving relations between their anomalies and confirming duality at the 1-loop level.

Contribution

It introduces a formalism based on Ward identities to analyze quantum T-duality beyond conformal backgrounds and applies it to specific non-Abelian and Poisson-Lie dual models.

Findings

Quantum T duality holds at 1-loop for studied models.

Derived relations between Weyl anomalies of dual theories.

Formalism applicable beyond conformally invariant backgrounds.

Abstract

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl anomaly coefficients of the original and dual theories. The analysis is not restricted to conformally invariant backgrounds. The formalism is applied to the study of two examples. The first is a model based on SU(2) non-Abelian T duality. The second represents a simple realization of Poisson-Lie T duality involving the Drinfeld double based on SU(2). In both cases quantum T duality is established at the 1-loop level.