José Figueroa-O'Farrill

A New maximally supersymmetric background of IIB superstring theory

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.

Penrose limits and maximal supersymmetry

We show that the maximally supersymmetric pp-wave of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS × S solutions. In addition, we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS × S background is either Minkowski space or a maximally supersymmetric pp-wave.

Penrose limits, supergravity and brane dynamics

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS ? S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalization to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born?Infeld type.

Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities

We classify (up to local isometry) the maximally supersymmetric solutions of the eleven- and ten-dimensional supergravity theories. We find that the AdS solutions, the Hpp-waves and the flat space solutions exhaust them.

Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory

We find M-theory solutions with homogeneous fluxes for which the spacetime is a lorentzian symmetric space. We show that generic solutions preserve sixteen supersymmetries and that there are two special points in their moduli space of parameters which preserve all thirty-two supersymmetries. We calculate the symmetry superalgebra of all these solutions. We then construct various M-theory and string theory branes with homogeneous fluxes and we also find new homogeneous flux-brane solutions.

On the supersymmetries of Anti-de Sitter vacua

We present details of a geometric method to associate a Lie superalgebra with a large class of bosonic supergravity vacua of the type AdS x X, corresponding to elementary branes in M-theory and type II string theory.

Breaking the M waves

We present a systematic attempt at a classification of supersymmetric -theory solutions with zero flux; that is, 11-dimensional Lorentzian manifolds with vanishing Ricci curvature and admitting parallel spinors. We show that there are two distinct classes of solutions: static spacetimes generalizing the Kaluza-Klein monopole and non-static spacetimes generalizing the supersymmetric wave. The classification can be further refined by the holonomy group of the spacetime. The static solutions are organized according to the holonomy group of the spacelike hypersurface, whereas the non-static solutions are similarly organized by the (Lorentzian) holonomy group of the spacetime. These are subgroups of the Lorentz group which act reducibly yet indecomposably on Minkowski spacetime. We present novel constructions of non-static solutions consisting of warped products of d-dimensional pp-waves with (11-d)-dimensional manifolds admitting parallel spinors. Our construction yields local metrics with a variety of exotic Lorentzian holonomy groups.We present a systematic attempt at classification of supersymmetric M-theory vacua with zero flux; that is, eleven-dimensional lorentzian manifolds with vanishing Ricci curvature and admitting covariantly constant spinors. We show that there are two distinct classes of solutions: static spacetimes generalising the Kaluza-Klein monopole, and non-static spacetimes generalising the supersymmetric wave. The classification can be further refined by the holonomy group of the spacetime. The static solutions are organised according to the holonomy group of the spacelike hypersurface, whereas the non-static solutions are similarly organised by the (lorentzian) holonomy group of the spacetime. These are subgroups of the Lorentz group which act reducibly yet indecomposably on Minkowski spacetime. We present novel constructions of non-static vacua consisting of warped products of d-dimensional pp-waves with (11-d)-dimensional manifolds admitting covariantly constant spinors. Our construction yields local metrics with a variety of exotic lorentzian holonomy groups. In the process, we write down the most general local metric in d<6 dimensions describing a pp-wave admitting a covariantly constant spinor. Finally, we also discuss a particular class of supersymmetric vacua with nonzero four-form obtained from the previous ones without modifying the holonomy of the metric. This is possible because in a lorentzian spacetime a metric which admits parallel spinors is not necessarily Ricci-flat, hence supersymmetric backgrounds need not satisfy the equations of motion.

Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space

We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are either one-dimensional, simple or in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N3/2 behaviour.

Metric Lie 3-algebras in Bagger-Lambert theory

We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2,p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2,p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.

Supersymmetry and homogeneity of M-theory backgrounds

We describe the construction of a Lie superalgebra associated with an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous. Furthermore we provide evidence that 24 is the minimal number of supersymmetries which guarantees this.