Double Field Theory and Membrane Sigma-Models

Understand

We investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model.

• Starting from the standard Courant algebroid over the phase space of an open membrane, we determine a splitting and a projection to a subbundle that sends the Courant algebroid operations to the corresponding operations in DFT.
• This describes precisely how the geometric structure of DFT lies in between two Courant algebroids and is reconciled with generalized geometry.
• We construct the membrane sigma-model that corresponds to DFT, and demonstrate how the standard T-duality orbit of geometric and non-geometric flux backgrounds is captured by its action functional in a unified way.