The homogeneity theorem for supergravity backgrounds

We prove the strong homogeneity conjecture for eleven- and ten-dimensional (Poincar\'e) supergravity backgrounds. In other words, we show that any backgrounds of 11-dimensional, type I/heterotic or type II supergravity theories preserving a fraction greater than one half of the supersymmetry of the underlying theory are necessarily locally homogeneous. Moreover we show that the homogeneity is due precisely to the supersymmetry, so that at every point of the spacetime one can find a frame for the tangent space made out of Killing vectors constructed out of the Killing spinors.Comment: 8 page

Lorentzian Lie n-algebras

We classify Lie n-algebras possessing an invariant lorentzian inner product.Comment: 10 pages (V2: more details on Section 3 and a new lemma. V3: typos corrected

A geometric construction of the exceptional Lie algebras F4 and E8

We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)Comment: 12 page

Pluecker-type relations for orthogonal planes

We explore a Pluecker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Pluecker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n-Lie algebra. In low dimension we present evidence for a geometric characterisation of the relation in terms of middle-dimensional orthogonal planes in euclidean or lorentzian inner product spaces.Comment: 39 pages (v2: substantial revision, 33% more material, link with n-Lie algebras

Classification of IIB backgrounds with 28 supersymmetries

We show that all IIB backgrounds with strictly 28 supersymmetries are locally isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we demonstrate that all solutions with more than 26 supersymmetries and only 5-form flux are maximally supersymmetric. The N=28 plane wave solution is a superposition of the maximally supersymmetric IIB plane wave with a heterotic string solution. We investigate the propagation of strings in this background, find the spectrum and give the string light-cone Hamiltonian.Comment: 30 pages, typos correcte

Three-Algebras and N=6 Chern-Simons Gauge Theories

We derive the general form for a three-dimensional scale-invariant field theory with N=6 supersymmetry, SU(4) R-symmetry and a U(1) global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not antisymmetric. For a specific choice of 3-algebra we obtain the N=6 theories that have been recently proposed as models for M2-branes in an R^8/Z_k orbifold background.Comment: 19 pages. Typos correcte

On the structure of symmetric self-dual Lie algebras

A finite-dimensional Lie algebra is called (symmetric) self-dual, if it possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric self-dual Lie algebras have been studied by Medina and Revoy, who have proven a very useful theorem about their structure. In this paper we prove a refinement of their theorem which has wide applicability in Conformal Field Theory, where symmetric self-dual Lie algebras start to play an important role due to the fact that they are precisely the Lie algebras which admit a Sugawara construction. We also prove a few corollaries which are important in Conformal Field Theory. (This paper provides mathematical details of results used, but only sketched, in the companion paper hep-th/9506151.)Comment: 19 pages, .dvi.uu (needs AMSFonts 2.1+

Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories

We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k, -k). The scaling limit (and Inonu-Wigner contraction) is to scale the trace part of the bifundamental fields as X_0 -> \lambda^{-1} X_0 and an axial combination of the two gauge fields as B_{\mu} -> \lambda B_\mu. Simultaneously we scale the level as k -> \lambda^{-1} k and then take \lambda -> 0 limit. Interestingly the same constraint equation \partial^2 X_0=0 is derived by imposing finiteness of the action. In this scaling limit, M2-branes are located far from the origin of C^4/Z_k compared to their fluctuations and Z_k identification becomes a circle identification. Hence the scaled theory describes N=8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X_0^I and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO(8) with the transformation of the background fields X_0^I.Comment: 21 pages; v2 a subsection added to discuss Generalized Conformal Invariance; v3 discussions on gravity dual added; v4 published version in PR

M2-branes, Einstein manifolds and triple systems

This is the written version of a talk given on 1 July 2009 at the XXV Max Born Symposium: the Planck Scale, held in Wroclaw, Poland. I review the possible transverse geometries to supersymmetric M2-brane configurations and discuss the representation-theoretic description of their conjectured dual superconformal Chern-Simons theories.Comment: 12 pages; V2: reference(s) adde

Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra

We summarise the results of our recent paper (arXiv:1511.08737) highlighting what might be considered to be a Lie-algebraic derivation of eleven-dimensional supergravity.Comment: 5 pages (v2: new title, added one reference, final version to appear in J. Phys A