Global Aspects of T-Duality, Gauged Sigma Models and T-Folds

TL;DR

This paper revisits the global aspects of T-duality in string theory, exploring obstructions, non-geometric backgrounds, and the extension of T-duality beyond isometric cases, with implications for T-fold topology.

Contribution

It extends T-duality derivations to non-isometric backgrounds and analyzes the topology of T-folds, considering global and topological obstructions.

Findings

T-duality can be applied even when sigma-models cannot be gauged.

Obstructions to gauging are milder than those to T-duality.

Conditions for T-dual backgrounds to be geometric are identified.

Abstract

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.