2015/09/30 by Pascal du Bosque, Falk Haßler, Falk Hassler +2
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant transformation #Embedding #Geometry #Group (periodic table) #Lie algebra #Lie group #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Twist #hep-th
paper · pdf · doi:10.1007/jhep02(2016)039
published as Journal of High Energy Physics, 2016(2), 1-41 · 40 pages, no figures, minor changes, published version
openalex publication_date 2016/02/01 · arxiv created 2016/02/12 · arxiv updated 2016/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, 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 2D-dimensional, 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 E A I ∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz 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, E A I is identified with the left invariant Maurer-Cartan form on the group manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3, 3), we calculate E A I .