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

Massive Type II in Double Field Theory

We provide an extension of the recently constructed double field theory formulation of the low-energy limits of type II strings, in which the RR fields can depend simultaneously on the 10-dimensional space-time coordinates and linearly on the dual winding coordinates. For the special case that only the RR one-form of type IIA carries such a dependence, we obtain the massive deformation of type IIA supergravity due to Romans. For T-dual configurations we obtain a `massive' but non-covariant formulation of type IIB, in which the 10-dimensional diffeomorphism symmetry is deformed by the mass parameter.Comment: 21 page

Double Field Theory Formulation of Heterotic Strings

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D,D+n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D,D+n) covariant fashion, in analogy to similar constructions in gauged supergravities.Comment: 28 pages, v2: minor changes, version published in JHE

On factorizations in perturbative quantum gravity

Some features of Einstein gravity are most easily understood from string theory but are not manifest at the level of the usual Lagrangian formulation. One example is the factorization of gravity amplitudes into gauge theory amplitudes. Based on the recently constructed `double field theory' and a geometrical frame-like formalism developed by Siegel, we provide a framework of perturbative Einstein gravity coupled to a 2-form and a dilaton in which, as a consequence of T-duality, the Feynman rules factorize to all orders in perturbation theory. We thereby establish the precise relation between the field variables in different formulations and discuss the Lagrangian that, when written in terms of these variables, makes a left-right factorization manifest.Comment: 18 pages, v2: reference added, to appear in JHE

Invariances and Equations of Motion in Double Field Theory

We investigate the full set of equations of motion in double field theory and discuss their O(D,D) symmetry and gauge transformation properties. We obtain a Ricci-like tensor, its associated Bianchi identities, and relate our results to those with a generalized metric formulation.Comment: 24 page

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

Ramond-Ramond Cohomology and O(D,D) T-duality

In the name of supersymmetric double field theory, superstring effective actions can be reformulated into simple forms. They feature a pair of vielbeins corresponding to the same spacetime metric, and hence enjoy double local Lorentz symmetries. In a manifestly covariant manner --with regard to O(D,D) T-duality, diffeomorphism, B-field gauge symmetry and the pair of local Lorentz symmetries-- we incorporate R-R potentials into double field theory. We take them as a single object which is in a bi-fundamental spinorial representation of the double Lorentz groups. We identify cohomological structure relevant to the field strength. A priori, the R-R sector as well as all the fermions are O(D,D) singlet. Yet, gauge fixing the two vielbeins equal to each other modifies the O(D,D) transformation rule to call for a compensating local Lorentz rotation, such that the R-R potential may turn into an O(D,D) spinor and T-duality can flip the chirality exchanging type IIA and IIB supergravities.Comment: 1+37 pages, no figure; Structure reorganized, References added, To appear in JHEP. cf. Gong Show of Strings 2012 (http://wwwth.mpp.mpg.de/members/strings/strings2012/strings_files/program/Talks/Thursday/Gongshow/Lee.pdf

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

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