T-Duality without Quantum Corrections

TL;DR

This paper investigates whether classical T-duality can be an exact quantum symmetry in N=4 supersymmetric sigma models, finding that quantum corrections generally modify T-duality except in specific geometric cases.

Contribution

It demonstrates that T-duality transformations in N=4 models typically receive quantum corrections, except for certain warped product geometries.

Findings

Quantum corrections generally modify T-duality transformations.

N=4 models with torsion are not off-shell finite quantum theories.

Warped products of flat submanifolds are exceptions where T-duality remains exact.

Abstract

It is a well known fact that the classical (``Buscher'') transformations of T-duality do receive, in general, quantum corrections. It is interesting to check whether classical T-duality can be exact as a quantum symmetry. The natural starting point is a $\sigma$-model with N=4 world sheet supersymmetry. Remarkably, we find that (owing to the fact that N=4 models with torsion are not off-shell finite as quantum theories),the T-duality transformations for these models get in general quantum corrections, with the only known exception of warped products of flat submanifolds or orbifolds thereof with other geometries.