We show, in two complementary ways, that D=11 supergravity-in contrast to all its lower dimensional versions-forbids a cosmological extension. First, we linearize the putative model about an Anti de Sitter background and show that it cannot even support a "global" supersymmetry invariance; hence there is no Noether construction that can lead to a local supersymmetry. This is true with the usual 4−form field as well as for a "dual", 7-form, starting point. Second, a cohomology argument, starting from the original full nonlinear theory, establishes the absence of deformations involving spin 3/2 mass and cosmological terms. In both approaches, it is the form field that is responsible for the obstruction. "Dualizing" the cosmological constant to an 11-form field also fails.
Anti-de Sitter supergravity models are considered in three dimensions. Precise asymptotic conditions involving a chiral projection are given on the Rarita-Schwinger fields. Together with the known boundary conditions on the bosonic fields, these ensure that the asymptotic symmetry algebra is the superconformal algebra. The classical central charge is computed and found to be equal to the one of pure gravity. It is also indicated that the asymptotic degrees of freedom are described by 2D "induced supergravity" and that the boundary conditions "transmute" the non-vanishing components of the WZW supercurrent into the supercharges.2
Asymptotically anti-de Sitter space-times in pure gravity with negative cosmological constant are described, in all space-time dimensions greater than two, by classical degrees of freedom on the conformal boundary at space-like infinity. Their effective boundary action has a conformal anomaly for even dimensions and is conformally invariant for odd ones. These degrees of freedom are encoded in traceless tensor fields in the Fefferman-Graham asymptotic metric for any choice of conformally flat boundary and generate all Schwarzschild and Kerr black holes in anti-de Sitter space-time. We argue that these fields describe components of an energy-momentum tensor of a boundary theory and show explicitly how this is realized in 2+1 dimensions. There, the Fefferman-Graham fields reduce to the generators of the Virasoro algebra and give the mass and the angular momentum of the BTZ black holes. Their local expression is the Liouville field in a general curved background.
It is shown that the AdS 3 gravity action with boundary terms is non invariant under diffeomorphisms and that its Lie derivative has the form of the Weyl anomaly in two dimensions. This variation is compensated by a Weyl transformation of the boundary metric when the radial derivative of the metric on the boundary is expressed in terms of the stress tensor of a Liouville field. The obtained invariance of the action under the combined transformation of a diffeomorphism and a Weyl transformation allows to interpret the computed Lie derivative as minus the Weyl anomaly of the two-dimensional effective action.1 Presented at the TMR European program meeting "Quantum aspects of gauge theories, supersymmetry and unification", ENS,
The Chern-Simons formulation of AdS3 supergravity is considered. Asymptotic conditions on the Rarita-Schwinger fields are given. Together with the known boundary conditions on the bosonic fields, these ensure that the asymptotic algebra is the superconformal algebra, with the same central charge as the one of pure gravity. It is also indicated that the asymptotic dynamics is described by super-Liouville.It has been pointed out in [1] that the asymptotic symmetry group of anti-de Sitter gravity in three dimensions is the conformal group in two dimensions with a central charge c = 3l/2G. This result was obtained by working out explicitly the boundary conditions and solving the asymptotic Killing equations [1]. It has been shown in [2] that the boundary dynamics at infinity is described by Liouville theory up to terms involving the zero modes and the holonomies that were not worked out. In the following, we will use the Chern-Simons formulation of AdS 3 (1,1)supergravity and extend the analysis of [1, 2] to the supersymmetric case. This was originally presented in [3] written in collaboration with M. Bañados, O. Coussaert, M. Henneaux and M. Ortiz and we refer to it for more details.Chern-Simons action. AdS 3 (1,1)-supergravity can be written as a Chern-Simons theory [4]. The relevant group is OSp(1|2) × OSp(1|2) and the action is: * ULB-TH-99/16
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