362 research outputs found
On the Riemann Tensor in Double Field Theory
Double field theory provides T-duality covariant generalized tensors that are
natural extensions of the scalar and Ricci curvatures of Riemannian geometry.
We search for a similar extension of the Riemann curvature tensor by developing
a geometry based on the generalized metric and the dilaton. We find a duality
covariant Riemann tensor whose contractions give the Ricci and scalar
curvatures, but that is not fully determined in terms of the physical fields.
This suggests that \alpha' corrections to the effective action require \alpha'
corrections to T-duality transformations and/or generalized diffeomorphisms.
Further evidence to this effect is found by an additional computation that
shows that there is no T-duality invariant four-derivative object built from
the generalized metric and the dilaton that reduces to the square of the
Riemann tensor.Comment: 36 pages, v2: minor changes, ref. added, v3: appendix on frame
formalism added, version to appear in JHE
The local symmetries of M-theory and their formulation in generalised geometry
In the doubled field theory approach to string theory, the T-duality group is
promoted to a manifest symmetry at the expense of replacing ordinary Riemannian
geometry with generalised geometry on a doubled space. The local symmetries are
then given by a generalised Lie derivative and its associated algebra. This
paper constructs an analogous structure for M-theory. A crucial by-product of
this is the derivation of the physical section condition for M-theory
formulated in an extended space.Comment: 20 pages, v2: Author Name corrected, v3: typos correcte
A Double Sigma Model for Double Field Theory
We define a sigma model with doubled target space and calculate its
background field equations. These coincide with generalised metric equation of
motion of double field theory, thus the double field theory is the effective
field theory for the sigma model.Comment: 26 pages, v1: 37 pages, v2: references added, v3: updated to match
published version - background and detail of calculations substantially
condensed, motivation expanded, refs added, results unchange
Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
We consider the reduction of the duality invariant approach to M-theory by a
U-duality group valued Scherk-Schwarz twist. The result is to produce
potentials for gauged supergravities that are normally associated with
non-geometric compactifications. The local symmetry reduces to gauge
transformations with the gaugings exactly matching those of the embedding
tensor approach to gauged supergravity. Importantly, this approach now includes
a nontrivial dependence of the fields on the extra coordinates of the extended
space.Comment: 22 pages Latex; v2: typos corrected and references adde
N=1 Supersymmetric Double Field Theory
We construct the N=1 supersymmetric extension of double field theory for
D=10, including the coupling to an arbitrary number n of abelian vector
multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space
symmetry under which the fermions transform. It is shown that the supersymmetry
transformations close into the generalized diffeomorphisms of double field
theory.Comment: 22 pages, v2: minor corrections, ref. added, to appear in JHE
Large Gauge Transformations in Double Field Theory
Finite gauge transformations in double field theory can be defined by the
exponential of generalized Lie derivatives. We interpret these transformations
as `generalized coordinate transformations' in the doubled space by proposing
and testing a formula that writes large transformations in terms of derivatives
of the coordinate maps. Successive generalized coordinate transformations give
a generalized coordinate transformation that differs from the direct
composition of the original two. Instead, it is constructed using the Courant
bracket. These transformations form a group when acting on fields but,
intriguingly, do not associate when acting on coordinates.Comment: 40 pages, v2: discussion of dilaton added, to appear in JHE
Gauged Double Field Theory
We find necessary and sufficient conditions for gauge invariance of the
action of Double Field Theory (DFT) as well as closure of the algebra of gauge
symmetries. The so-called weak and strong constraints are sufficient to satisfy
them, but not necessary. We then analyze compactifications of DFT on twisted
double tori satisfying the consistency conditions. The effective theory is a
Gauged DFT where the gaugings come from the duality twists. The action,
bracket, global symmetries, gauge symmetries and their closure are computed by
twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic
string and lower dimensional gauged supergravities are particular examples of
Gauged DFT.Comment: Minor changes, references adde
On massive gravitons in 2+1 dimensions
The Fierz-Pauli (FP) free field theory for massive spin 2 particles can be
extended, in a spacetime of (1+2) dimensions (3D), to a generally covariant
parity-preserving interacting field theory, in at least two ways. One is "new
massive gravity" (NMG), with an action that involves curvature-squared terms.
Another is 3D "bigravity", which involves non-linear couplings of the FP tensor
field to 3D Einstein-Hilbert gravity. We review the proof of the linearized
equivalence of both "massive 3D gravity" theories to FP theory, and we comment
on their similarities and differences.Comment: 6 pages, to appear in the proceedings of the Spanish Relativity
Meeting ERE2009, Bilbao; minor changes, reference adde
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