On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model

In this note we consider a fermionic T-duality of the coset realization of the type IIA sigma-model on AdS_4 \times CP^3 with respect to the three flat directions in AdS_4, six of the fermionic coordinates and three of the CP^3 directions. We show that the Buscher procedure fails as it leads to a singular transformation and discuss the result and its implications.Comment: LaTeX2e, 9 pages, no figures, JHEP style; v2: minor clarifications; v3: typos fixed, matches the published versio

Differential geometry with a projection: Application to double field theory

In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D) rotation. In this paper, we conceive a differential geometry characterized by a O(D,D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O(D,D) vector indices.Comment: 1+22 pages, No figure; a previous result on 4-index tensor removed, presentation improve

Non-abelian T-duality, Ramond Fields and Coset Geometries

We extend previous work on non-abelian T-duality in the presence of Ramond fluxes to cases in which the duality group acts with isotropy such as in backgrounds containing coset spaces. In the process we generate new supergravity solutions related to D-brane configurations and to standard supergravity compactifications.Comment: 35 pages, Late

Background independent action for double field theory

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.Comment: 45 pages, v2: minor corrections, refs. added, to appear in JHE

Fermionic T-duality in the pp-wave limit

AdS5 X S5 and its pp-wave limit are self-dual under transformations involving eight fermionic T-dualities, a property which accounts for symmetries seen in scattering amplitudes in N=4 super-Yang-Mills. Despite strong evidence for similar symmetries in the amplitudes of three-dimensional N=6 ABJM theory, a corresponding self-duality in the dual geometry AdS4 X CP3 currently eludes us. Here, working with the type IIA pp-wave limit of AdS4 X CP3 preserving twenty four supercharges, we show that the pp-wave is self-dual with respect to eight commuting fermionic T-dualities and not the six expected. In addition, we show the same symmetry can be found in a superposition pp-wave and a generic pp-wave with twenty and sixteen unbroken supersymmetries respectively, strongly suggesting that self-duality under fermionic T-duality may be a symmetry of all pp-waves.Comment: 21 pages, typos fixe

T-duality and closed string non-commutative (doubled) geometry

We provide some evidence that closed string coordinates will become non-commutative turning on H-field flux background in closed string compactifications. This is in analogy to open string non-commutativity on the world volume of D-branes with B- and F-field background. The class of 3-dimensional backgrounds we are studying are twisted tori (fibrations of a 2-torus over a circle) and the their T-dual H-field, 3-form flux backgrounds (T-folds). The spatial non-commutativity arises due to the non-trivial monodromies of the toroidal Kahler resp. complex structure moduli fields, when going around the closed string along the circle direction. In addition we study closed string non-commutativity in the context of doubled geometry, where we argue that in general a non-commutative closed string background is T-dual to a commutative closed string background and vice versa. Finally, in analogy to open string boundary conditions, we also argue that closed string momentum and winding modes define in some sense D-branes in closed string doubled geometry.Comment: 31 pages, references added, extended version contains new sections 3.3., 3.4 and

Classification of non-Riemannian doubled-yet-gauged spacetime

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon these backgrounds, strings become chiral and anti-chiral over $n$ and $\bar{n}$ directions respectively, while particles and strings are frozen over the $n+\bar{n}$ directions. In particular, we identify $(0,0)$ as Riemannian manifolds, $(1,0)$ as non-relativistic spacetime, $(1,1)$ as Gomis-Ooguri non-relativistic string, $(D{-1},0)$ as ultra-relativistic Carroll geometry, and $(D,0)$ as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, $(0,1)$ leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as $D=10$, $(3,3)$ may open a new scheme of the dimensional reduction from ten to four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in (2.51) correcte

Smeared versus localised sources in flux compactifications

We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p+1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution with smeared orientifolds and the localised version is worked out in detail. We then demonstrate that a class of non-BPS AdS_4 solutions that exist for IASD fluxes and with smeared D3-branes (or analogously for ISD fluxes with anti-D3-branes) does not survive the localisation of the (anti) D3-branes. This casts doubts on the stringy consistency of non-BPS solutions that are obtained in the limit of smeared sources.Comment: 23 pages; v2: minor corrections, added references, version published in JHE

Hypermoduli Stabilization, Flux Attractors, and Generating Functions

We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be integrated by a generating function with the property that the hypermoduli are determined by a simple extremization principle. We work out several orbifold examples where all vector moduli and many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.Comment: 45 pages, no figures; Version submitted to JHE