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 [1].
Highlights
We describe the doubled space of Double Field Theory as a group manifold G with an arbitrary generalized metric
We reproduce the topology changes induced by T-duality with non-trivial H-flux which were discussed by Bouwknegt, Evslin and Mathai [1]
We show that ηij = 0 automatically holds if: first, we choose a coset representative of the form m = exp[f (xi)] with f : U → m where U denotes a patch of the physical subspace G/H
Summary
In the following we review the features of DFTWZW [33, 34] which are essential to discuss non-trivial solutions of the SC. In general there are different ways how to choose this canonical form They are all related by GL(2d) transformations. The DFTWZW action (2.5) is invariant under generalized diffeomorphisms They are generated by the generalized Lie derivative. · is a place holder for fields, parameters of generalized diffeomorphisms and arbitrary products of them This constraint requires that all fields only depend on a ddimensional subspace M of the doubled space. In addition to generalized diffeomorphisms, the action and the generalized Lie derivative transform covariantly under 2d-diffeomorphisms. There, the doubled space does not carry any additional structures besides generalized diffeomorphisms
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