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

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

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

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

Spinorial geometry and Killing spinor equations of 6-D supergravity

We solve the Killing spinor equations of 6-dimensional (1,0)-supergravity coupled to any number of tensor, vector and scalar multiplets in all cases. The isotropy groups of Killing spinors are Sp(1)\cdot Sp(1)\ltimes \bH (1), U(1)\cdot Sp(1)\ltimes \bH (2), Sp(1)\ltimes \bH (3,4), $Sp(1) (2)$, $U(1) (4)$ and $\{1\} (8)$, where in parenthesis is the number of supersymmetries preserved in each case. If the isotropy group is non-compact, the spacetime admits a parallel null 1-form with respect to a connection with torsion the 3-form field strength of the gravitational multiplet. The associated vector field is Killing and the 3-form is determined in terms of the geometry of spacetime. The Sp(1)\ltimes \bH case admits a descendant solution preserving 3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If the isotropy group is compact, the spacetime admits a natural frame constructed from 1-form spinor bi-linears. In the $Sp(1)$ and U(1) cases, the spacetime admits 3 and 4 parallel 1-forms with respect to the connection with torsion, respectively. The associated vector fields are Killing and under some additional restrictions the spacetime is a principal bundle with fibre a Lorentzian Lie group. The conditions imposed by the Killing spinor equations on all other fields are also determined.Comment: 34 pages, Minor change

Birkhoff's Theorem for Three-Dimensional AdS Gravity

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual Coussaert-Henneaux spacetimes, with isometry groups SO(2) x SO(2,1) or SO(2) x SO(2).Comment: 11 pages, RevTeX4; minor typos corrected, Ref. added, accepted for publication in Phys. Rev.

Uniqueness of M-theory PP-Wave Background with Extra Supersymmetries

We examine Killing spinor equations of the general eleven-dimensional pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a three-form \xi(x^m,x^-) in the flux. Considering non-harmonic extra Killing spinors, we show that if the backgrounds admit at least one extra Killing spinor in addition to the standard 16 Killing spinors, they can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-) modulo coordinate transformations. We further examine the cases in which the extra Killing spinor is characterized by a set of Cartan matrices. The super-isometry algebras of the resulting backgrounds are also derived.Comment: 25 pages, LaTeX2e, comments added, version to appear in PR

Multiple M2-branes and Generalized 3-Lie algebras

We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss how to associate various ordinary Lie algebras.Comment: 1+19 pages, version published in Phys. Rev.