Diederik Roest

Systematics of IIB spinorial geometry

We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of Gran et al (2005 Class. Quantum Grav. 22 118 (Preprint hep-th/0503046)) to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the Killing spinors. This system can be solved to express the fluxes in terms of the geometry and determine the conditions on the geometry of any supersymmetric background. Similarly, the integrability conditions of the Killing spinor equations are turned into a linear system. This can be used to determine the field equations that are implied by the Killing spinor equations for any supersymmetric background. We show that these linear systems simplify for generic backgrounds with maximal and half-maximal number of H-invariant Killing spinors, H ⊂ Spin(9, 1). In the maximal case, the Killing spinor equations factorize, whereas in the half-maximal case they do not. As an example, we solve the Killing spinor equations of backgrounds with two -invariant Killing spinors. We also solve the linear systems associated with the integrability conditions of maximally supersymmetric —and —backgrounds and determine the field equations that are not implied by the Killing spinor equations.

N=31 is not IIB

We adapt the spinorial geometry method to investigate supergravity backgrounds with near maximal number of supersymmetries. We then apply the formalism to show that the IIB supergravity backgrounds with 31 supersymmetries preserve an additional supersymmetry and so they are maximally supersymmetric. This rules out the existence of IIB supergravity preons.

Systematics of M-theory spinorial geometry

We reduce the classification of all supersymmetric backgrounds in 11 dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We determine the expression of the supercovariant derivative on all six types of spinors and give in each case the field equations that do not arise as the integrability conditions of Killing spinor equations. The Killing spinor equations of a background become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the spinors. The solution of the linear system expresses the fluxes in terms of the geometry and specifies the restrictions on the geometry of spacetime for all supersymmetric backgrounds. We also show that the minimum number of field equations that is needed for a supersymmetric configuration to be a solution of 11-dimensional supergravity can be found by solving a linear system. The linear systems of the Killing spinor equations and their integrability conditions are given in both a timelike and a null spinor basis. We illustrate the construction with examples.

Transient quintessence from group manifold reductions or how all roads lead to Rome

We investigate the accelerating phases of cosmologies supported by a metric, scalars and a single exponential scalar potential. The different solutions can be represented by trajectories on a sphere and we find that quintessence happens within the arctic circle of the sphere. Furthermore, we obtain multi-exponential potentials from 3D group manifold reductions of gravity, implying that such potentials can be embedded in gauged supergravities with an M-theory origin. We relate the double exponential case to flux compactifications on maximally symmetric spaces and S-branes. In the triple exponential case our analysis suggests the existence of two exotic S(D - 3)-branes in D dimensions.

Non-extremal D-instantons

We construct the most general non-extremal deformation of the D-instanton solution with maximal rotational symmetry. The general non-supersymmetric solution carries electric charges of the SL(2,) symmetry, which correspond to each of the three conjugacy classes of SL(2,). Our calculations naturally generalise to arbitrary dimensions and arbitrary dilaton couplings. We show that for specific values of the dilaton coupling parameter, the non-extremal instanton solutions can be viewed as wormholes of non-extremal Reissner-Nordstrom black holes in one higher dimension. We extend this result by showing that for other values of the dilaton coupling parameter, the non-extremal instanton solutions can be uplifted to non-extremal non-dilatonic p-branes in p+1 dimensions higher. Finally, we attempt to consider the solutions as instantons of (compactified) type-IIB superstring theory. In particular, we derive an elegant formula for the instanton action. We conjecture that the non-extremal D-instantons can contribute to the R8-terms in the type-IIB string effective action.

Maximally Supersymmetric G-Backgrounds of IIB Supergravity

We classify the geometry of all supersymmetric IIB backgrounds which admit the maximal number of G-invariant Killing spinors. For compact stability subgroups G = G2, SU(3) and SU(2), the spacetime is locally isometric to a product Xn × Y10−n with n = 3, 4, 6, where Xn is a maximally supersymmetric solution of a n-dimensional supergravity theory and Y10−n is a Riemannian manifold with holonomy G. For non-compact stability subgroups, G = K ⋉ R8, K = Spin(7), SU(4), Sp(2), SU(2) × SU(2) and {1}, the spacetime is a pp-wave propagating in an eight-dimensional manifold with holonomy K. We find new supersymmetric pp-wave solutions of IIB supergravity.

Classical resolution of singularities in dilaton cosmologies

For models of dilaton gravity with a possible exponential potential, such as the tensor–scalar sector of IIA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to points at which a trajectory meets the Milne horizon, but the trajectories can be smoothly continued through the horizon to an instanton solution of the Euclidean theory. We find some exact cosmology/instanton solutions that lift to black holes in one higher dimension. For one such solution, the singularities of a big crunch to big bang transition mediated by an instanton phase lift to the black hole and cosmological horizons of de Sitter Schwarzschild spacetimes.

Cosmological D-instantons and cyclic universes

For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the augmented target space connect FLRW cosmologies to non-extremal D-instantons through a cosmological singularity. In particular, we find closed cyclic universes that undergo an endless sequence of big-bang to big-crunch cycles separated by instanton phases. We also find big-bounce universes in which a collapsing closed universe bounces off its cosmological singularity to become an open expanding universe.

Brane Solutions of Gravity–Dilaton–Axion Systems

We consider general properties of brane solutions of gravity‐dilaton‐axion systems. We focus on the case of 7‐branes and instantons. In both cases we show that besides the standard solutions there are new deformed solutions whose charges take value in any of the three conjugacy classes of SL(2, R). In the case of 7‐branes we find that for each conjugacy class the 7‐brane solutions are 1/2 BPS. Next, we discuss the relation of the 7‐branes with the DW/QFT correspondence. In particular, we show that the two (inequivalent) 7‐brane solutions in the SO(2) conjugacy class have a nice interpretation as a distribution of (the so‐called near horizon limit of) branes. This suggests a way to define the near‐horizon limit of a 7‐brane.In the case of instantons only the solutions corresponding to the R conjugacy class are 1/2 BPS. The solutions corresponding to the other two conjugacy classess correspond to non‐extremal deformations. We first discuss an alternative description of these solutions as the geodesic motion...