T-duality in an H-flux: exchange of momentum and winding

TL;DR

This paper extends the mathematical framework of T-duality in string theory with H-flux by incorporating exotic differential forms, revealing an exchange between momentum and winding numbers and enhancing the understanding of T-duality's geometric structure.

Contribution

It generalizes the Hori isomorphism to exotic differential forms and extends Courant algebroid actions to these forms, filling a key gap in the mathematical understanding of T-duality with H-flux.

Findings

Exchange of momentum and winding numbers in exotic differential forms.

Extension of Hori isomorphism to invariant exotic forms.

Compatibility of Courant algebroid actions with T-duality.

Abstract

Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space, we extend the Hori isomorphism of Bouwknegt-Evslin-Mathai from invariant differential forms, to invariant exotic differential forms such that the momentum and winding numbers are exchanged, filling in a gap in the literature. We also extend the compatibility of the action of invariant exact Courant algebroids on the T-duality isomorphism of Cavalcanti-Gualtieri, to the T-duality isomorphism on exotic invariant differential forms.