Topology and Flux of T-Dual Manifolds with Circle Actions

TL;DR

This paper derives an explicit formula for the topology and H-flux of T-duals in type II string theory with circle actions, revealing singularities and proposing classification of charges via twisted equivariant cohomology and K-theory.

Contribution

It generalizes previous T-duality results to arbitrary circle actions and introduces a classification scheme for Ramond-Ramond charges on singular dual spaces.

Findings

T-dual spaces can be singular when fixed points are present.

Ramond-Ramond charges are classified by twisted equivariant cohomology.

K-theory provides an alternative classification approach.

Abstract

We present an explicit formula for the topology and H-flux of the T-dual of a general type II compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime. As before, T-duality exchanges type IIA and type IIB string theories. A new consequence is that the T-dual spacetime is a singular space when the fixed point set is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II string theories on the singular dual are classified by twisted equivariant cohomology groups. We also include the K-theory approach.