The exceptional generalised geometry of supersymmetric AdS flux backgrounds

We analyse generic AdS flux backgrounds preserving eight supercharges in $D=4$ and $D=5$ dimensions using exceptional generalised geometry. We show that they are described by a pair of globally defined, generalised structures, identical to those that appear for flat flux backgrounds but with different integrability conditions. We give a number of explicit examples of such "exceptional Sasaki-Einstein" backgrounds in type IIB supergravity and M-theory. In particular, we give the complete analysis of the generic AdS$_5$ M-theory backgrounds. We also briefly discuss the structure of the moduli space of solutions. In all cases, one structure defines a "generalised Reeb vector" that generates a Killing symmetry of the background corresponding to the R-symmetry of the dual field theory, and in addition encodes the generic contact structures that appear in the $D=4$ M-theory and $D=5$ type IIB cases. Finally, we investigate the relation between generalised structures and quantities in the dual field theory, showing that the central charge and R-charge of BPS wrapped-brane states are both encoded by the generalised Reeb vector, as well as discussing how volume minimisation (the dual of $a$- and $\mathcal{F}$-maximisation) is encoded.Comment: 40 page

On the Evaluation of Compton Scattering Amplitudes in String Theory

We consider the Compton amplitude for the scattering of a photon and a (massless) ``electron/positron'' at one loop (i.e. genus one) in a four-dimensional fermionic heterotic string model. Starting from the bosonization of the world-sheet fermions needed to explicitly construct the spin-fields representing the space-time fermions, we present all the steps of the computation which leads to the explicit form of the amplitude as an integral of modular forms over the moduli space.Comment: 41 pages, Late

Non-Relativistic Solutions of N=2 Gauged Supergravity

We find infinite families of supersymmetric solutions of four dimensional, N=2 gauged supergravity with Lifshitz, Schrodinger and also AdS symmetries. We focus on the canonical example of a single hypermultiplet and a single vector multiplet and find that the spectrum of solutions depends crucially on whether the gaugings are electric or magnetic but to a far milder extent on the strength of the gaugings. For purely electric or purely magnetic gaugings we generically find Lifshitz solutions, while for a mixed gauging we find Schrodinger and AdS solutions. For some of the gaugings the theory has a known lift to string/M-theory thus giving a higher dimensional embedding of our solutions.Comment: 27 pages, v2 refs added, comments regarding string embeddings altered, cleaner discussion of the scaling parameter for Schrodinger solutions; v3 published version, refs adde

BPS Black Holes in AdS4 from M-theory

We study supersymmetric black holes in $AdS_4$ in the framework of four dimensional gauged $\N=2$ supergravity coupled to hypermultiplets. We derive the flow equations for a general electrically gauged theory where the gauge group is Abelian and, restricting them to the fixed points, we derive the gauged supergravity analogue of the attractor equations for theories coupled to hypermultiplets. The particular models we analyze are consistent truncations of M-theory on certain Sasaki-Einstein seven-manifolds. We study the space of horizon solutions of the form $AdS_2\times \Sigma_g$ with both electric and magnetic charges and find a four-dimensional solution space when the theory arises from a reduction on $Q^{111}$. For other $SE_7$ reductions, the solutions space is a subspace of this. We construct explicit examples of spherically symmetric black holes numerically.Comment: 38 page, 4 figures; typos correcte

The Enhancon and N=2 Gauge Theory/Gravity RG Flows

We study the family of ten dimensional type IIB supergravity solutions corresponding to renormalisation group flows from N=4 to N=2 supersymmetric Yang-Mills theory. Part of the solution set corresponds to a submanifold of the Coulomb branch of the gauge theory, and we use a D3-brane probe to uncover details of this physics. At generic places where supergravity is singular, the smooth physics of the probe yields the correct one-loop form of the effective low energy gauge coupling. The probe becomes tensionless on a ring at finite radius. Supergravity flows which end on this ``enhancon'' ring correspond to the vacua where extra massless degrees of freedom appear in the gauge theory, and the gauge coupling diverges there. We identify an SL(2,Z) duality action on the enhancon ring which relates the special vacua, and comment on the massless dyons within them. We propose that the supergravity solution inside the enhancon ring should be excised, since the probe's tension is unphysical there.Comment: 25 pages, 3 composite figures, LaTex (v2: reference added. clarifying footnote added. typos corrected, with addition to discussion of BPS dyons in section 7.

A scan for new N=1 vacua on twisted tori

We perform a systematic search for N=1 Minkowski vacua of type II string theories on compact six-dimensional parallelizable nil- and solvmanifolds (quotients of six-dimensional nilpotent and solvable groups, respectively). Some of these manifolds have appeared in the construction of string backgrounds and are typically called twisted tori. We look for vacua directly in ten dimensions, using the a reformulation of the supersymmetry condition in the framework of generalized complex geometry. Certain algebraic criteria to establish compactness of the manifolds involved are also needed. Although the conditions for preserved N=1 supersymmetry fit nicely in the framework of generalized complex geometry, they are notoriously hard to solve when coupled to the Bianchi identities. We find solutions in a large-volume, constant-dilaton limit. Among these, we identify those that are T-dual to backgrounds of IIB on a conformal T^6 with self-dual three-form flux, and hence conceptually not new. For all backgrounds of this type fully localized solutions can be obtained. The other new solutions need multiple intersecting sources (either orientifold planes or combinations of O-planes and D-branes) to satisfy the Bianchi identities; the full list of such new solution is given. These are so far only smeared solutions, and their localization is yet unknown. Although valid in a large-volume limit, they are the first examples of Minkowski vacua in supergravity which are not connected by any duality to a Calabi-Yau. Finally, we discuss a class of flat solvmanifolds that may lead to AdS_4 vacua of type IIA strings.Comment: 75 pages, 1 figure. v.2: minor corrections, references added; v3: several changes and clarification

Nontrivial RR two-form field strength and SU(3)-structure

We discuss how in the presence of a nontrivial RR two-form field strength and nontrivial dilaton the conditions of preserving supersymmetry on six-dimensional manifolds lead to generalized monopole and Killing spinor equations. We show that the manifold is K\"ahler in the ten-dimensional string frame if F_0^{(1,1)}=0. We then determine explicitly the intrinsic torsion of the SU(3)-structure on six-manifolds that result via Kaluza-Klein reduction from seven-manifolds with G_2-structure of generic intrinsic torsion. Lastly we give explicitly the intrinsic torsion of the SU(3)-structure for an N=1 supersymmetric background in the presence of nontrivial RR two-form field strength and nontrivial dilaton.Comment: LaTeX, 8 pages, talk given at the 35th Symposium Ahrenshoop, enlarged version of the contribution to the proceeding

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