Renormalisability of non-homogeneous T-dualised sigma-models

TL;DR

This paper investigates the quantum equivalence of non-homogeneous sigma-models and their non-abelian T-duals, establishing conditions for their one-loop renormalisability and analyzing their geometric properties.

Contribution

It proves the equivalence of one-loop renormalisability between original and T-dual sigma-models for a broad class of metrics, including non-homogeneous and quasi-Einstein cases.

Findings

Renormalisability is preserved under non-abelian T-duality for the studied models.

Dual models retain Kahler structure in certain subclasses.

The results apply to models with SU(2)×U(1) isometry group.

Abstract

The quantum equivalence between sigma-models and their non-abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group SU(2) times U(1). We prove that the one-loop renormalisability of the initial torsionless sigma-models is equivalent to the one-loop renormalisability of the T-dualised torsionful model. For a subclass of Kahler original metrics, the dual partners are still Kahler (with torsion).