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

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+

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

Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature.Comment: 62 pages, 3 figures, 4 tables, v2: Matches published version, mistake corrected in Section 4.1.3., 10.2, 10.3, other minor improvements, added reference

Quotients of AdS_{p+1} x S^q: causally well-behaved spaces and black holes

Starting from the recent classification of quotients of Freund--Rubin backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved causal structures, and of those containing closed timelike curves, which have interpretations as black holes. We explain the relation to previous investigations of quotients of asymptotically flat spacetimes and plane waves, of black holes in AdS and of Godel-type universes.Comment: 48 pages; v2: minor typos correcte

Homogeneous M2 duals

Motivated by the search for new gravity duals to M2 branes with $N>4$ supersymmetry --- equivalently, M-theory backgrounds with Killing superalgebra $\mathfrak{osp}(N|4)$ for $N>4$ --- we classify homogeneous M-theory backgrounds with symmetry Lie algebra $\mathfrak{so}(n) \oplus \mathfrak{so}(3,2)$ for $n=5,6,7$. We find that there are no new backgrounds with $n=6,7$ but we do find a number of new (to us) backgrounds with $n=5$. All backgrounds are metrically products of the form $\operatorname{AdS}_4 \times P^7$, with $P$ riemannian and homogeneous under the action of $\operatorname{SO}(5)$, or $S^4 \times Q^7$ with $Q$ lorentzian and homogeneous under the action of $\operatorname{SO}(3,2)$. At least one of the new backgrounds is supersymmetric (albeit with only $N=2$) and we show that it can be constructed from a supersymmetric Freund--Rubin background via a Wick rotation. Two of the new backgrounds have only been approximated numerically. (The second version of this paper includes an appendix by Alexander~S.~Haupt, closing a gap in our original analysis.)Comment: 56 page

On BPS preons, generalized holonomies and D=11 supergravities

We develop the BPS preon conjecture to analyze the supersymmetric solutions of D=11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G=GL(32,R), SL(32,R) or Sp(32,R)) to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (31/32) solutions of the standard D=11 supergravity. We also show that there exist elementary preonic solutions, i.e. solutions preserving 31 out of 32 supersymmetries in a Chern--Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D'Auria-Fre type OSp(1|32)-related supergravity model. We discuss the possible implications for M-theory.Comment: 11 pages, RevTeX Typos corrected, a short note and references adde

Supersymmetry of hyperbolic monopoles

We investigate what supersymmetry says about the geometry of the moduli space of hyperbolic monopoles. We construct a three-dimensional supersymmetric Yang-Mills-Higgs theory on hyperbolic space whose half-BPS configurations coincide with (complexified) hyperbolic monopoles. We then study the action of the preserved supersymmetry on the collective coordinates and show that demanding closure of the supersymmetry algebra constraints the geometry of the moduli space of hyperbolic monopoles, turning it into a so-called pluricomplex manifold, thus recovering a recent result of Bielawski and Schwachh\"ofer.Comment: 22 page