On black hole thermodynamics from super Yang-Mills

We consider maximally supersymmetric U(N) Yang-Mills in (1+p)-dimensions for p < 3. In the 't Hooft large N limit this is conjectured to be dual to N Dp-branes in the decoupling limit. At low temperatures T << \lambda^{1/(3-p)} governed by the dimensionful 't Hooft coupling \lambda, supergravity black holes predict the free energy density goes as ~ N^2 T^{2(7-p)/(5-p)} and the expectation value of the scalars goes as ~ T^{2/(5-p)}, with dimensions made up by \lambda. The purpose of this work is to explain the origin of these peculiar powers of temperature. We argue that these powers naturally arise by requiring that the low energy moduli of the theory become strongly coupled at low temperature. As an application, we consider the BMN quantum mechanics that results from a supersymmetric deformation of the p=0 theory. The black holes dual to this deformed theory have not yet been constructed, and our analysis can be used to make an explicit prediction for their thermodynamic behaviour.Comment: 28 pages, no figures. v2: journal version - minor corrections, references adde

Gauge-gravity duality -- Super Yang Mills Quantum Mechanics

We describe the conjectured holographic duality between Yang-Mills quantum mechanics and type IIa string theory. This duality allows us to use lattice Monte Carlo simulations to probe the physics of the gravitational theory - for example, at low energies it provides a computation of black hole entropy in terms of a sum over microstates of the dual gauge theory. Numerical results are presented of the 4 supercharge theory at finite temperatureComment: 7 pages, 6 figures, Talk at lattice 200

A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow

Entanglement entropies are notoriously difficult to compute. Large-N strongly-coupled holographic CFTs are an important exception, where the AdS/CFT dictionary gives the entanglement entropy of a CFT region in terms of the area of an extremal bulk surface anchored to the AdS boundary. Using this prescription, we show -- for quite general states of (2+1)-dimensional such CFTs -- that the renormalized entanglement entropy of any region of the CFT is bounded from above by a weighted local energy density. The key ingredient in this construction is the inverse mean curvature (IMC) flow, which we suitably generalize to flows of surfaces anchored to the AdS boundary. Our bound can then be thought of as a "subregion" Penrose inequality in asymptotically locally AdS spacetimes, similar to the Penrose inequalities obtained from IMC flows in asymptotically flat spacetimes. Combining the result with positivity of relative entropy, we argue that our bound is valid perturbatively in 1/N, and conjecture that a restricted version of it holds in any CFT.Comment: 33+7 pages, 7 figures. v2: addressed referee comment

Properties of Kaluza-Klein black holes

We detail numerical methods to compute the geometry of static vacuum black holes in 6 dimensional gravity compactified on a circle. We calculate properties of these Kaluza-Klein black holes for varying mass, while keeping the asymptotic compactification radius fixed. For increasing mass the horizon deforms to a prolate ellipsoid, and the geometry near the horizon and axis decompactifies. We are able to find solutions with horizon radii approximately equal to the asymptotic compactification radius. Having chosen 6-dimensions, we may compare these solutions to the non-uniform strings compactified on the same radius of circle found in previous numerical work. We find the black holes achieve larger masses and horizon volumes than the most non-uniform strings. This sheds doubt on whether these solution branches can merge via a topology changing solution. Further work is required to resolve whether there is a maximum mass for the black holes, or whether the mass can become arbitrarily large.Comment: 33 pages, 13 colour figures; v2 minor corrections and some figures beautifie

On Universality of Holographic Results for (2+1)-Dimensional CFTs on Curved Spacetimes

The behavior of holographic CFTs is constrained by the existence of a bulk dual geometry. For example, in (2+1)-dimensional holographic CFTs living on a static spacetime with compact spatial slices, the vacuum energy must be nonpositive, certain averaged energy densities must be nonpositive, and the spectrum of scalar operators is bounded from below by the Ricci scalar of the CFT geometry. Are these results special to holographic CFTs? Here we show that for perturbations about appropriate backgrounds, they are in fact universal to all CFTs, as they follow from the universal behavior of two- and three-point correlators of known operators. In the case of vacuum energy, we extend away from the perturbative regime and make global statements about its negativity properties on the space of spatial geometries. Finally, we comment on the implications for dynamics which are dissipative and driven by such a vacuum energy and we remark on similar results for the behavior of the Euclidean partition function on deformations of flat space or the round sphere.Comment: 35+4 pages, 1 figure. v2: corrected discussion of torus to deformed flat space; additional comments adde

Plasma-balls in large N gauge theories and localized black holes

We argue for the existence of plasma-balls - meta-stable, nearly homogeneous lumps of gluon plasma at just above the deconfinement energy density - in a class of large N confining gauge theories that undergo first order deconfinement transitions. Plasma-balls decay over a time scale of order N^2 by thermally radiating hadrons at the deconfinement temperature. In gauge theories that have a dual description that is well approximated by a theory of gravity in a warped geometry, we propose that plasma-balls map to a family of classically stable finite energy black holes localized in the IR. We present a conjecture for the qualitative nature of large mass black holes in such backgrounds, and numerically construct these black holes in a particular class of warped geometries. These black holes have novel properties; in particular their temperature approaches a nonzero constant value at large mass. Black holes dual to plasma-balls shrink as they decay by Hawking radiation; towards the end of this process they resemble ten dimensional Schwarzschild black holes, which we propose are dual to small plasma-balls. Our work may find practical applications in the study of the physics of localized black holes from a dual viewpoint.Comment: harvmac, 33 pages + 7 appendices + 14 figures; program code downloadable from http://schwinger.harvard.edu/~wiseman/IRblackholes ; v2: minor changes ; v3: refs added, minor change