T-duality for principal torus bundles
Peter Bouwknegt, Keith Hannabuss, Varghese Mathai
TL;DR
The paper extends T-duality from principal circle bundles to principal $\mathsf T^n$-bundles with $H$-flux by identifying a class of T-dualizable fluxes and constructing explicit dual geometries and fluxes. It introduces invariant, $\hat{\mathfrak t}$-valued 2-forms $\widehat{F}$ that determine dual bundles $\widehat{E}$ and derives a dual flux $\widehat{H}$ on $\widehat{E}$ using a correspondence space, yielding Buscher-like maps between twisted cohomology and twisted K-theory. A generalized RW-cohomology framework with a corresponding Gysin sequence ties the cohomologies of $(E,H)$ and $(\widehat{E},\widehat{H})$, clarifying when dualities live inside the principal torus-bundle category. The work provides explicit dualities for group manifolds and related examples, illustrating both the reach and the limitations of T-duality in the presence of $H$-flux and guiding future investigations into broader flux configurations.
Abstract
In this paper we study T-duality for principal torus bundles with H-flux. We identify a subset of fluxes which are T-dualizable, and compute both the dual torus bundle as well as the dual H-flux. We briefly discuss the generalized Gysin sequence behind this construction and provide examples both of non T-dualizable and of T-dualizable H-fluxes.