Non-geometric fluxes versus (non)-geometry

Non-geometry has been introduced when considering a new type of string backgrounds, for which stringy symmetries serve as transition functions between patches of the target space. Then, some terms in the potential of four-dimensional gauged supergravities, generated by so-called non-geometric fluxes, have been argued to find a higher-dimensional origin in these backgrounds, even if a standard compactification on those cannot be made. We present here recent results clarifying the relation between these two settings. Thanks to a field redefinition, we reformulate the NSNS Lagrangian in such a way that the non-geometric fluxes appear in ten dimensions. In addition, if an NSNS field configuration is non-geometric, its reformulation in terms of the new fields can restore a standard geometry. A dimensional reduction is then possible, and leads to the non-geometric terms in the four-dimensional potential. Reformulating similarly doubled field theory, we get a better understanding of the role of the non-geometric fluxes, and rewrite the Lagrangian in a manifestly diffeomorphism-covariant manner. We finally discuss the relevance of the field redefinition and the non-geometric fluxes when studying the non-commutativity of string coordinates.Comment: 12 pages; this paper is based on a talk given at String-Math 2012 in Bonn, Germany, and contributes to the proceedings of this conference; v2: references added; v3: published versio

New supersymmetric vacua on solvmanifolds

We obtain new supersymmetric flux vacua of type II supergravities on four-dimensional Minkowski times six-dimensional solvmanifolds. The orientifold O4, O5, O6, O7, or O8-planes and D-branes are localized. All vacua are in addition not T-dual to a vacuum on the torus. The corresponding solvmanifolds are proven to be Calabi-Yau, with explicit metrics. Other Ricci flat solvmanifolds are shown to be only K\"ahler.Comment: v2: few additions and minor modifications, published versio

Refining the boundaries of the classical de Sitter landscape

We derive highly constraining no-go theorems for classical de Sitter backgrounds of string theory, with parallel sources; this should impact the embedding of cosmological models. We study ten-dimensional vacua of type II supergravities with parallel and backreacted orientifold Op-planes and Dp-branes, on four-dimensional de Sitter space-time times a compact manifold. Vacua for p=3, 7 or 8 are completely excluded, and we obtain tight constraints for p=4, 5, 6. This is achieved through the derivation of an enlightening expression for the four-dimensional Ricci scalar. Further interesting expressions and no-go theorems are obtained. The paper is self-contained so technical aspects, including conventions, might be of more general interest.Comment: 15 pages + appendices and references; v2: few additions; v3: requirements on the sources and internal geometry clarified, version accepted for publication; v4: erratum added, minor impact on the result

NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes

In the first half of the paper, we study in details NS-branes, including the NS5-brane, the Kaluza-Klein monopole and the exotic $5_2^2$- or Q-brane, together with Bianchi identities for NSNS (non)-geometric fluxes. Four-dimensional Bianchi identities are generalized to ten dimensions with non-constant fluxes, and get corrected by a source term in presence of an NS-brane. The latter allows them to reduce to the expected Poisson equation. Without sources, our Bianchi identities are also recovered by squaring a nilpotent $Spin(D,D) \times \mathbb{R}^+$ Dirac operator. Generalized Geometry allows us in addition to express the equations of motion explicitly in terms of fluxes. In the second half, we perform a general analysis of ten-dimensional geometric backgrounds with non-geometric fluxes, in the context of $\beta$-supergravity. We determine a well-defined class of such vacua, that are non-geometric in standard supergravity: they involve $\beta$-transforms, a manifest symmetry of $\beta$-supergravity with isometries. We show as well that these vacua belong to a geometric T-duality orbit.Comment: v2: minor changes and additions, few references added, published versio

Signatures of extra dimensions in gravitational waves

Considering gravitational waves propagating on the most general 4+N-dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski4 times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.Comment: v1: 21 pages + appendices, comments welcome! v2: few minor additions; v3: minor mistake corrected in the warped case, no impact on the main results, appendix A.2 modifie

Bumping into the species scale with the scalar potential

As a quantum gravity cut-off, the species scale $\Lambda_s$ gets naturally compared to the energy scale of a scalar potential $V$ in an EFT. In this note, we compare the species scale, its rate $|\nabla \Lambda_s|/\Lambda_s$ and their field dependence, to those of a scalar potential. To that end, we first identify a string compactification leading to a scalar potential with the same properties as the species scale, namely, being positive, starting at a maximum in the bulk of field space and going asymptotically to zero. The trajectory followed in our 14-fields scalar potential is the steepest descent. Evaluating the rate $|\nabla V|/V$ along this path, we then observe a local maximum, or bump, a feature noticed as well for the species scale. We investigate the origin of this bump for the scalar potential, and compare it to that of the species scale.Comment: v2: minor modification

Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory

We consider IIA compactifications on solvmanifolds with O6/D6 branes and study the conditions for obtaining de Sitter vacua in ten dimensions. While this is a popular set-up for searching de Sitter vacua, we propose a new method to include supersymmetry breaking sources. For space-time filling branes preserving bulk supersymmetry, the energy density can easily be extremized with respect to all fields, thanks to the replacement of the DBI action by a pullback of a special form given by a pure spinor. For sources breaking bulk supersymmetry, we propose to replace the DBI action by the pullback of a more general polyform, which is no longer pure. This generalization provides corrections to the energy-momentum tensor which give a positive contribution to the cosmological constant. We find a de Sitter solution to all (bulk and world-volume) equations derived from this action. We argue it solves the equations derived from the standard source action. The paper also contains a review of solvmanifolds.Comment: 57 pages, 3 figures. Important additions (concerning the validity of our solution in string theory); version to appear in JHE