46 research outputs found
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
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
(), the spin connection (), two gravitini
() and an gauge connection (). These
fields form a connection for . In eleven dimensions the theory is an
N=1 supergravity containing, apart from and ,
one gravitino , and a totally antisymmetric fifth rank Lorentz
tensor one-form, . These fields form a connection for
. The actions are by construction invariant under local
supersymmetry and the algebra closes off shell without requiring auxiliary
fields. The -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.
Ambient metrics for -dimensional -waves
We provide an explicit formula for the Fefferman-Graham-ambient metric of an
-dimensional conformal -wave in those cases where it exists. In even
dimensions we calculate the obstruction explicitly. Furthermore, we describe
all 4-dimensional -waves that are Bach-flat, and give a large class of
Bach-flat examples which are conformally Cotton-flat, but not conformally
Einstein. Finally, as an application, we use the obtained ambient metric to
show that even-dimensional -waves have vanishing critical -curvature.Comment: 17 pages, in v2 footnote and references added and typos corrected, in
v3 remark in the Introduction about Brinkmann's results corrected and
footnote adde