The Topology of Double Field Theory

TL;DR

This paper explores the topology of the doubled space in Double Field Theory, modeling it as a group manifold and analyzing its maximal isotropic submanifolds, revealing topology changes under T-duality with flux.

Contribution

It constructs the doubled space as a group manifold and analyzes its maximal isotropic submanifolds, demonstrating topology changes under T-duality with flux.

Findings

Reproduces topology changes induced by T-duality with flux

Constructs generalized geometry on group manifolds

Shows different physical subspaces related by Poisson-Lie T-duality

Abstract

We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold $M$ in $G$. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, $G$ admits different physical subspace $M$ which are Poisson-Lie T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial $H$-flux which were discussed by Bouwknegt, Evslin and Mathai [hep-th/0306062].