du Bosque, Pascal; Hassler, Falk; Lüst, Dieter
(2016):
Flux formulation of DFT on group manifolds and generalized ScherkSchwarz compactifications.
In: Journal of High Energy Physics, No. 2, 039

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Abstract
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized ScherkSchwarz compactifications, which give rise to a bosonic subsector of halfmaximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2Ddimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O(D, D). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein EA(I) is an element of GL(2 D). This vielbein takes the role of the twist in conventional generalized ScherkSchwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, EA(I) is identified with the left invariant MaurerCartan form on the group manifold, in the same way as it is done in geometric ScherkSchwarz reductions. We show in detail how the MaurerCartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3, 3), we calculate EA(I).