Topological T-duality via Lie algebroids and $Q$-flux in Poisson-generalized geometry

TL;DR

This paper reformulates topological T-duality as an exchange of Lie algebroids within generalized geometry and extends this to Poisson-generalized geometry, revealing a duality between R-flux and Q-flux.

Contribution

It introduces a novel Lie algebroid exchange perspective on T-duality and defines Q-flux in Poisson-generalized geometry, expanding the understanding of flux dualities.

Findings

T-duality exchanges H and F-fluxes.

T-duality exchanges R-flux and Q-flux in Poisson-generalized geometry.

New definition of Q-flux associated with β-diffeomorphisms.

Abstract

It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In this paper, we reformulate the topological T-duality as an exchange of two Lie algebroids in the generalized tangent bundle. Then, we apply the same formulation to the Poisson-generalized geometry, which is introduced in arXiv:1408.2649 to define $R$-fluxes as field strength associated with $\beta$-transformations. We propose a definition of $Q$-flux associated with $\beta$-diffeomorphisms, and show that the topological T-duality exchanges $R$ and $Q$-fluxes.