Stability in Einstein-Scalar Gravity with a Logarithmic Branch

We investigate the non-perturbative stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass saturating the Breitenlohner-Freedman bound. Such "designer gravity" theories admit a large class of boundary conditions at asymptotic infinity. At this mass, the asymptotic behavior of the scalar field develops a logarithmic branch, and previous attempts at proving a minimum energy theorem failed due to a large radius divergence in the spinor charge. In this paper, we finally resolve this issue and derive a lower bound on the conserved energy. Just as for masses slightly above the BF bound, a given scalar potential can admit two possible branches of the corresponding superpotential, one analytic and one non-analytic. The key point again is that existence of the non-analytic branch is necessary for the energy bound to hold. We discuss several AdS/CFT applications of this result, including the use of double-trace deformations to induce spontaneous symmetry breaking.Comment: 31 pages, 7 figure

Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-3/2 Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in AdS_4. Linear Rarita-Schwinger fields in AdS_d are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0 \leq |m| < 1/2l_{AdS}$. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is "renormalized" accordingly with the action. We then use the results obtained for |m| = 1/l_{AdS} to explore supersymmetric boundary conditions for N = 1 AdS_4 supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in d=4 supergravity correspond to gauging the superconformal group of the 3-dimensional CFT describing M2-branes, while N = 1 supersymmetric mixed boundary conditions couple the CFT to N = 1 superconformal topologically massive gravity.Comment: 23 pages, RevTe

A note on Kerr/CFT and free fields

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2,R) x U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.Comment: 10 pages, v2: comments and references adde

A tale of two superpotentials: Stability and Instability in Designer Gravity

We investigate the stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. Previous work had suggested that the energy in designer gravity is bounded below if i) W has a global minimum and ii) the scalar potential admits a superpotential P. More recently, however, certain solutions were found (numerically) to violate the proposed energy bound. We resolve the discrepancy by observing that a given scalar potential can admit two possible branches of the corresponding superpotential, P_{\pm}. When there is a P_- branch, we rigorously prove a lower bound on the energy; the P_+ branch alone is not sufficient. Our numerical investigations i) confirm this picture, ii) confirm other critical aspects of the (complicated) proofs, and iii) suggest that the existence of P_- may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below

Near Extremal Kerr Entropy from AdS_2 Quantum Gravity

We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro algebra with central charge c_R=12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy's formula to determine the near extremal entropy. Our result is consistent with the Bekenstein-Hawking area law for near extremal Kerr black holes.Comment: 28 pages. v2: references added, typos correcte

Particle dynamics near extreme Kerr throat and supersymmetry

The extreme Kerr throat solution is believed to be non-supersymmetric. However, its isometry group SO(2,1) x U(1) matches precisely the bosonic subgroup of N=2 superconformal group in one dimension. In this paper we construct N=2 supersymmetric extension of a massive particle moving near the horizon of the extreme Kerr black hole. Bosonic conserved charges are related to Killing vectors in a conventional way. Geometric interpretation of supersymmetry charges remains a challenge.Comment: V2: 10 pages; discussion in sect. 4 and 5 extended, acknowledgements and references adde

On the CFT duals for near-extremal black holes

We consider Kerr-Newman-AdS-dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U(1)_L x U(1)_R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well defined and non-vanishing and to yield central charges c_L\neq0 and c_R=0. The Cardy formula subsequently reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr-Newman-AdS-dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.Comment: 11 page

A near-NHEK/CFT correspondence

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U(1)_L x U(1)_R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and non-vanishing and find the central charges c_L=12J/hbar and c_R=0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a non-chiral two-dimensional conformal field theory.Comment: 11 pages, v2: references updated, adde

From Unruh temperature to generalized Bousso bound

In a classical spacetime satisfying Einstein's equation and the null convergence condition, the same quantum mechanical effects that cause black holes to have a temperature are found to imply, if joined to the macroscopic nature of entropy, the covariant entropy bound in its generalized form. This is obtained from thermodynamics, as applied across the local Rindler causal horizon through every point p of the null hypersurfaces L the covariant entropy bound refers to, in the direction of the null geodesics generating L.Comment: 5 pages. v2: some changes to clarify the path to the obtained results; two (final) paragraphs, the acknowledgments and a reference adde

No Dynamics in the Extremal Kerr Throat

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.Comment: 42 pages, 3 figures. v3: minor clarifications and correction