Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification added, typos corrected, to appear in JHE

Lovelock theories, holography and the fate of the viscosity bound

We consider Lovelock theories of gravity in the context of AdS/CFT. We show that, for these theories, causality violation on a black hole background can occur well in the interior of the geometry, thus posing more stringent constraints than were previously found in the literature. Also, we find that instabilities of the geometry can appear for certain parameter values at any point in the geometry, as well in the bulk as close to the horizon. These new sources of causality violation and instability should be related to CFT features that do not depend on the UV behavior. They solve a puzzle found previously concerning unphysical negative values for the shear viscosity that are not ruled out solely by causality restrictions. We find that, contrary to previous expectations, causality violation is not always related to positivity of energy. Furthermore, we compute the bound for the shear viscosity to entropy density ratio of supersymmetric conformal field theories from d=4 till d=10 - i.e., up to quartic Lovelock theory -, and find that it behaves smoothly as a function of d. We propose an approximate formula that nicely fits these values and has a nice asymptotic behavior when d goes to infinity for any Lovelock gravity. We discuss in some detail the latter limit. We finally argue that it is possible to obtain increasingly lower values for the shear viscosity to entropy density ratio by the inclusion of more Lovelock terms.Comment: 42 pages, 17 figures, JHEP3.cls. v2: reference adde

Viscosity Bound and Causality in Superfluid Plasma

It was argued by Brigante et.al that the lower bound on the ratio of the shear viscosity to the entropy density in strongly coupled plasma is translated into microcausality violation in the dual gravitational description. Since transport properties of the system characterize its infrared dynamics, while the causality of the theory is determined by its ultraviolet behavior, the viscosity bound/microcausality link should not be applicable to theories that undergo low temperature phase transitions. We present an explicit model of AdS/CFT correspondence that confirms this fact.Comment: 27 pages, 5 figures. References added, typos fixe

The Weak Gravity Conjecture and the Viscosity Bound with Six-Derivative Corrections

The weak gravity conjecture and the shear viscosity to entropy density bound place constraints on low energy effective field theories that may help to distinguish which theories can be UV completed. Recently, there have been suggestions of a possible correlation between the two constraints. In some interesting cases, the behavior was precisely such that the conjectures were mutually exclusive. Motivated by these works, we study the mass to charge and shear viscosity to entropy density ratios for charged AdS5 black branes, which are holographically dual to four-dimensional CFTs at finite temperature. We study a family of four-derivative and six-derivative perturbative corrections to these backgrounds. We identify the region in parameter space where the two constraints are satisfied and in particular find that the inclusion of the next-to-leading perturbative correction introduces wider possibilities for the satisfaction of both constraints.Comment: 24 pages, 6 figures, v2: published version, refs added, minor clarificatio

Causality in AdS/CFT and Lovelock theory

We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS space-time. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.Comment: 35 pages, 20 figures; v2: minor amendments and clarifications include

Analytical study on holographic superconductors in external magnetic field

We investigate the holographic superconductors immersed in an external magnetic field by using the analytical approach. We obtain the spatially dependent condensate solutions in the presence of the magnetism and find analytically that the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. We observe analytically the reminiscent of the Meissner effect where the magnetic field expels the condensate. Extending to the D-dimensional Gauss-Bonnet AdS black holes, we examine the influence given by the Gauss-Bonnet coupling on the condensation. Different from the positive coupling, we find that the negative Gauss-Bonnet coupling enhances the condensation when the external magnetism is not strong enough.Comment: revised version, to appear in JHE

On the new massive gravity and AdS/CFT

Demanding the existence of a simple holographic $c$-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory. We consider extending the theory including upto six derivative curvature invariants. Black hole solutions are presented and consistency with 1+1 CFTs is checked. We present evidence that bulk unitarity is still in conflict with a positive CFT central charge for generic choice of parameters. However, for a special choice of parameters appearing in the four and six derivative terms reduces the linearized equations to be two derivative, thereby ameliorating the unitarity problem.Comment: 16 pages, 2 figures. v4: typo correcte

Black Holes in Quasi-topological Gravity

We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and higher-dimensional CFT's. We also investigate the black hole solutions of this new gravity theory. Further we examine the equations of motion of quasi-topological gravity. While the full equations in a general background are fourth-order in derivatives, we show that the linearized equations describing gravitons propagating in the AdS vacua match precisely the second-order equations of Einstein gravity.Comment: 33 pages, 4 figures; two references adde