T-duality of singular spacetime compactifications in an H-flux

TL;DR

This paper extends T-duality to singular spacetime compactifications with H-flux, using twisted equivariant cohomology and Courant algebroids, revealing new insights into string theory on singular spaces.

Contribution

It introduces a symmetric T-duality framework for singular spaces and develops twisted equivariant Courant algebroids and cohomology in this context.

Findings

T-duality exchanges type II A and B theories on singular spaces.

Ramond-Ramond charges are classified by twisted equivariant cohomology.

Isomorphism of twisted equivariant Courant algebroids established.

Abstract

We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalised geometry and apply it to our context. As before, T-duality exchanges type II A and type II B string theories. In our theory, both spacetime and the T-dual spacetime can be singular spaces 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 spaces are classified by twisted equivariant cohomology groups, consistent with the previous work of Mathai and Wu, and prove that they are naturally isomorphic. We also establish the corresponding isomorphism of twisted equivariant Courant algebroids.