Holographic studies of quasi-topological gravity

Quasi-topological gravity is a new gravitational theory including curvature-cubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be dual to the large $N_c$ limit of some non-supersymmetric but conformal gauge theory. We establish various elements of the AdS/CFT dictionary for this duality. This allows us to infer physical constraints on the couplings in the gravitational theory. Further we use holography to investigate hydrodynamic aspects of the dual gauge theory. In particular, we find that the minimum value of the shear-viscosity-to-entropy-density ratio for this model is $\eta/s \simeq 0.4140/(4\pi)$.Comment: 45 pages, 6 figures. v2: References adde

Entropy Bound and Causality Violation in Higher Curvature Gravity

In any quantum theory of gravity we do expect corrections to Einstein gravity to occur. Yet, at fundamental level, it is not apparent what the most relevant corrections are. We argue that the generic curvature square corrections present in lower dimensional actions of various compactified string theories provide a natural passage between the classical and quantum realms of gravity. The Gauss-Bonnet and $({\rm Riemann})^2$ gravities, in particular, provide concrete examples in which inconsistency of a theory, such as, a violation of microcausality, and a classical limit on black hole entropy are correlated. In such theories the ratio of the shear viscosity to the entropy density, $\eta/s$, can be smaller than for a boundary conformal field theory with Einstein gravity dual. This result is interesting from the viewpoint that the nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme densities and temperatures may violate the conjectured bound $\eta/s\ge 1/4\pi$, {\it albeit} marginally so.Comment: 23 pages, several eps figures; minor changes, references added, published versio

Holographic GB gravity in arbitrary dimensions

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.Comment: 48 pages, 9 figures. v2: New discussion on free fields in subsection 3.3 and new appendix B on conformal tensor fields. Added comments on the relation between the central charge appearing in the two-point function and the "central charge" characterizing the entropy density in the discussion. References adde

On higher derivative gravity, c-theorems and cosmology

We consider higher derivative gravity lagrangians in 3 and 4 dimensions, which admit simple c-theorems, including upto six derivative curvature invariants. Following a suggestion by Myers, these lagrangians are restricted such that the fluctuations around (anti) de Sitter spaces have second order linearized equations of motion. We study c-theorems both in the context of AdS/CFT and cosmology. In the context of cosmology, the monotonic function is the entropy defined on the apparent horizon through Wald's formula. Exact black hole solutions which are asymptotically (anti) de Sitter are presented. An interesting lower bound for entropy is found in de Sitter space. Some aspects of cosmology in both D=3 and D=4 are discussed.Comment: 23 pages, v3: clarifications added, references adde

Comments on Holographic Entanglement Entropy and RG Flows

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.Comment: References adde

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte

Holographic Hydrodynamics with a Chemical Potential

We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions perturbatively and consider the thermal and hydrodynamic properties of the plasma in the dual CFT. In particular, we calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential. We also compute the electrical conductivity and comment on various conjectured bounds related to this coefficient.Comment: v2: comparison to supergravity lagrangian added, references added, typos fixe