Dilaton transformation under abelian and non-abelian T-duality in the path integral approach

TL;DR

This paper develops a path-integral method to accurately derive the dilaton transformation under both abelian and non-abelian T-duality, clarifying previous ambiguities and extending the formalism to more general cases.

Contribution

It introduces a novel path-integral approach for dilaton transformation, including non-abelian T-duality, with improved regularization and gauge choices.

Findings

Clarified ambiguities in dilaton transformation derivations

Extended formalism to non-abelian T-duality cases

Identified weaker conditions for gauging non-abelian isometries

Abstract

We present a convenient method for deriving the transformation of the dilaton under T-duality in the path-integral approach. Subtleties arising in performing the integral over the gauge fields are carefully analysed using Pauli-Villars regularization, thereby clarifying existing ambiguities in the literature. The formalism can not only be applied to the abelian case, but, and this for the first time, to the non-abelian case as well. Furthermore, by choosing a particular gauge, we directly obtain the target-space covariant expression for the dual geometry in the abelian case. Finally it is shown that the conditions for gauging non-abelian isometries are weaker than those generally found in the literature.