Double Field Theory on Group Manifolds (Thesis)

TL;DR

This thesis extends Double Field Theory to group manifolds, deriving a generalized formalism that captures string dynamics on such backgrounds, and resolves key issues like flux formulation and twist construction.

Contribution

It introduces DFT_WZW, a generalization of DFT for group manifolds, with new gauge algebra, flux formulation, and solutions to longstanding problems in Scherk-Schwarz compactifications.

Findings

Derived the classical action and gauge transformations from String Field Theory.

Established a flux formulation and connected it to generalized Scherk-Schwarz compactifications.

Solved the problem of constructing the twist in generalized Scherk-Schwarz compactifications.

Abstract

This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$ space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFT${}_\mathrm{WZW}$, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold. 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 weaker closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the original formulation, DFT${}_\mathrm{WZW}$ is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the original 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, a long standing problem, the missing of a prescription to construct the twist in generalized Scherk-Schwarz compactifications, is solved. Altogether, a more general picture of DFT and the structures it is based on emerges.