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

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.

44 pages

References in corpus (3)

• Double Field Theory
• T-duality and closed string non-commutative (doubled) geometry
• Lectures on Nongeometric Flux Compactifications

Cited by in corpus (7)

• Generalised Kinematics for Double Field Theory
• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• DFT in supermanifold formulation and group manifold as background geometry
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
• The Algebroid Structure of Double Field Theory
• Brane current algebras and generalised geometry from QP manifolds
• Higher dimensional Lie algebroid sigma model with WZ term