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

Abstract

Using our earlier proposal for Ramond–Ramond fields in an H-flux on loop space (Han et al. in Commun Math Phys 337(1):127–150, 2015. arXiv:1405.1320), we extend the Hori isomorphism in Bouwknegt et al. (Commun Math Phys 249:383–415, 2004. arXiv:hep-th/0306062; Phys Rev Lett 92:181601, 2004. arXiv:hep-th/0312052) 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 in Cavalcanti and Gualtieri (in: CRM proceedings of lecture notes, vol 50, pp 341–365, American Mathematical Society, Providence, 2010 ), to the T-duality isomorphism on exotic invariant differential forms.