No Cosmological D=11 Supergravity

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

The Fefferman-Graham Ambiguity and AdS Black Holes

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.Comment: Latex, 14 pages; one reference modified, minor misprints correcte

Uniqueness of the asymptotic AdS3 geometry

We explicitly show that in (2+1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neigbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant. Gra

Diffeomorphisms and Holographic Anomalies

Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary we study the Weyl transformation properties of the bulk metric on shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.Comment: 12 pages, harvma

Massive type IIA string theory cannot be strongly coupled

Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in AdS4xCP3: one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N.Comment: 43 pages, 5 figures. v2: added reference

New Gauge Supergravity in Seven and Eleven Dimensions

Locally supersymmetric systems in odd dimensions whose Lagrangians are Chern-Simons forms for supersymmetric extensions of anti-de Sitter gravity are discussed. The construction is illustrated for D=7 and 11. In seven dimensions the theory is an N=2 supergravity whose fields are the vielbein ($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), two gravitini ($\psi_{\mu}^{i}$) and an $sp(2)$ gauge connection ($a_{\mu j}^{i}$). These fields form a connection for $osp(2|8)$. In eleven dimensions the theory is an N=1 supergravity containing, apart from $e_{\mu}^{a}$ and $\omega_{\mu}^{ab}$, one gravitino $\psi_{\mu}$, and a totally antisymmetric fifth rank Lorentz tensor one-form, $b_{\mu}^{abcde}$. These fields form a connection for $osp(32|1)$. The actions are by construction invariant under local supersymmetry and the algebra closes off shell without requiring auxiliary fields. The $N=2^{[D/2]}$-theory can be shown to have nonnegative energy around an AdS background, which is a classical solution that saturates the Bogomolnyi bound obtained from the superalgebra.Comment: 5pages, RevTeX, no figures, two columns, minor typos correcte

Black holes with topologically nontrivial AdS asymptotics

Asymptotically locally AdS black hole geometries of dimension d > 2 are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer 0 < k < [(d-1)/2] which possess a unique globally AdS vacuum. The transverse sections of these solutions are d-2 surfaces of constant curvature, allowing for different topological configurations. The thermodynamic analysis of these solutions reveals that the presence of a negative cosmological constant is essential to ensure the existence of stable equilibrium states. In addition, it is shown that these theories are holographically related to [(d-1)/2] different conformal field theories at the boundary.Comment: 13 Pages, 3 figures, two columns, Revtex, last version for PR

Black Hole Scan

Gravitation theories selected by requiring that they have a unique anti-de Sitter vacuum with a fixed cosmological constant are studied. For a given dimension d, the Lagrangians under consideration are labeled by an integer k=1,2,...,[(d-1)/2]. Black holes for each d and k are found and are used to rank these theories. A minimum possible size for a localized electrically charged source is predicted in the whole set of theories, except General Relativity. It is found that the thermodynamic behavior falls into two classes: If d-2k=1, these solutions resemble the three dimensional black hole, otherwise, their behavior is similar to the Schwarzschild-AdS_4 geometry.Comment: Two columns, revtex, 15 pages, 5 figures, minor typos corrected, final version for Journa

M-Theory as a Holographic Field Theory

We suggest that M-theory could be non-perturbatively equivalent to a local quantum field theory. More precisely, we present a ``renormalizable'' gauge theory in eleven dimensions, and show that it exhibits various properties expected of quantum M-theory, most notably the holographic principle of 't~Hooft and Susskind. The theory also satisfies Mach's principle: A macroscopically large space-time (and the inertia of low-energy excitations) is generated by a large number of ``partons'' in the microscopic theory. We argue that at low energies in large eleven dimensions, the theory should be effectively described by eleven-dimensional supergravity. This effective description breaks down at much lower energies than naively expected, precisely when the system saturates the Bekenstein bound on energy density. We show that the number of partons scales like the area of the surface surrounding the system, and discuss how this holographic reduction of degrees of freedom affects the cosmological constant problem. We propose the holographic field theory as a candidate for a covariant, non-perturbative formulation of quantum M-theory.Comment: 27 pp. v2: typos corrected; a small paragraph on naturalness of small cosmological constant in four dimensions added at end of sect 5.1; final version to appear in Phys. Rev.

Holography and the Polyakov action

In two dimensional conformal field theory the generating functional for correlators of the stress-energy tensor is given by the non-local Polyakov action associated with the background geometry. We study this functional holographically by calculating the regularized on-shell action of asymptotically AdS gravity in three dimensions, associated with a specified (but arbitrary) boundary metric. This procedure is simplified by making use of the Chern-Simons formulation, and a corresponding first-order expansion of the bulk dreibein, rather than the metric expansion of Fefferman and Graham. The dependence of the resulting functional on local moduli of the boundary metric agrees precisely with the Polyakov action, in accord with the AdS/CFT correspondence. We also verify the consistency of this result with regard to the nontrivial transformation properties of bulk solutions under Brown-Henneaux diffeomorphisms.Comment: 20 pages, RevTeX, v2: minor typos corrected and references adde