Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds

TL;DR

This paper systematically derives local expressions for various fluxes in double field theory using supergeometric methods, clarifies their Bianchi identities, and presents a T-duality formulation via graded symplectic manifolds.

Contribution

It introduces a supergeometric approach to derive flux expressions and formulate T-duality in double field theory, connecting fluxes with graded symplectic geometry.

Findings

Derived local flux expressions using supergeometry.

Presented a T-duality formulation via canonical transformations.

Compared the construction to the Poisson Courant algebroid model.

Abstract

We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector beta- and two-form B-potentials including vielbeins. They are obtained using a supergeometric method on QP-manifolds by twist of the standard Courant algebroid on the generalized tangent space without flux. Bianchi identities of the fluxes are easily deduced. We extend the discussion to the case of the double space and present a formulation of T-duality in terms of canonical transformations between graded symplectic manifolds. Finally, the construction is compared to the formerly introduced Poisson Courant algebroid, a Courant algebroid on a Poisson manifold, as a model for R-flux.