D-branes and doubled geometry

TL;DR

This paper develops an open string sigma model on doubled geometry, classifies D-branes within it, and demonstrates their behavior under T-duality transformations in flux backgrounds.

Contribution

It introduces a systematic method to derive and classify D-branes in doubled geometry, including boundary conditions and their transformations under T-duality.

Findings

Derived boundary conditions for open strings on doubled geometry.

Classified D-branes as maximally isotropic submanifolds.

Verified D-brane transformations under T-duality in flux backgrounds.

Abstract

We define the open string version of the nonlinear sigma model on doubled geometry introduced by Hull and Reid-Edwards, and derive its boundary conditions. These conditions include the restriction of D-branes to maximally isotropic submanifolds as well as a compatibility condition with the Lie algebra structure on the doubled space. We demonstrate a systematic method to derive and classify D-branes from the boundary conditions, in terms of embeddings both in the doubled geometry and in the physical target space. We apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and D2-branes, which we verify transform consistently under T-dualities mapping the system to f-, Q- and R-flux backgrounds.