Double field theory on group manifolds

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.