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Haßler, Falk (2015): Double field theory on group manifolds. Dissertation, LMU München: Fakultät für Physik



This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. All observables arising from those dynamics match on certain families of background space times. These different backgrounds are connected by T-duality. DFT renders T-duality on a torus manifest by adding D windig coordinates in addition to the D space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for fields which depend on half of the coordinates of the arising doubled space. An important application of DFT are generalized Scherk-Schwarz compactifications. They give rise to half-maximal, electrically gauged supergravities which are classified by the embedding tensor formalism, specifying the embedding of their gauge group into O(n,n). Because it is not compatible with all solutions of the embedding tensor, the strong constraint is replaced by the closure constraint of DFT's flux formulation. This allows for compactifications on backgrounds which are not T-dual to well-defined geometric ones. Their description requires non-geometric fluxes. Due to their special properties, they are also of particular phenomenological interest. However, the violation of the strong constraint obscures their uplift to full string theory. Moreover, there is an ambiguity in generalizing traditional Scherk-Schwarz compactifications to the doubled space of DFT: There is a lack of a general procedure to construct the twist of the compactification. After reviewing DFT and generalized Scherk-Schwarz compactifications, DFT_WZW, a generalization of the current formalism is presented. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold and it allows to solve the problems mentioned above. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constraint, while for the former the closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the traditional formulation, DFT_WZW is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the traditional formulation is restored. A flux formulation for the new theory is derived and its connection to generalized Scherk-Schwarz compactifications is discussed. Further, a possible tree-level uplift of a genuinely non-geometric background (not T-dual to any geometric configuration) is presented. Finally, the ambiguity in constructing the compactification's twist is eliminated. Altogether, a more general picture of DFT and the structures it is based on emerges.