On the Topology and Flux of T-Dual Manifolds

TL;DR

A general formula for the topology and H-flux of the T-dual of a type II compactification is presented, finding that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of theDual H- flux over the dual circle.

Abstract

We present a general formula for the topology and H-flux of the T-dual of a type two compactification. Our results apply to T-dualities with respect to any free circle action. In particular we find that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of the dual H-flux over the dual circle. As a corollary we conjecture an obstruction to multiple T-dualities, generalizing an obstruction known to exist on the twisted torus. Examples include SU(2) WZW models, Lens spaces and the supersymmetric string theory on the non-spin AdS^5xCP^2xS^1 compactification.