v2, Important additions: (1) discussion of the entropy current, (2) postulated zeta/eta bound is generically violated. Some comments and references added, typos corrected. 50 pagesInternational audienceWe show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related to higher dimensional AdS-Maxwell gravity via a dimensional reduction over compact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values ('generalized dimensional reduction'). This relates (fairly complicated) black hole solutions of EMD theories to simple black hole/brane solutions of AdS-Maxwell gravity and explains their properties. The generalized dimensional reduction is used to infer the holographic dictionary and the hydrodynamic behavior for this class of theories from those of AdS. As a specific example, we analyze the case of a black brane carrying a wave whose universal sector is described by gravity coupled to a Maxwell field and two neutral scalars. At thermal equilibrium and finite chemical potential the two operators dual to the bulk scalar fields acquire expectation values characterizing the breaking of conformal and generalized conformal invariance. We compute holographically the first order transport coefficients (conductivity, shear and bulk viscosity) for this system

Motivated by holography, we explore higher derivative corrections to four-dimensional Anti-de Sitter (AdS) gravity. We point out that in such a theory the variational problem is generically not well-posed given only a boundary condition for the metric. However, when one evaluates the higher derivative terms perturbatively on a leading order Einstein solution, the equations of motion are always second order and therefore the variational problem indeed requires only a boundary condition for the metric. The equations of motion required to compute the spectrum around the corrected background are still generically higher order, with the additional boundary conditions being associated with new operators in the dual conformal field theory. We discuss which higher derivative curvature invariants are expected to arise in the four-dimensional action from a top-down perspective and compute the corrections to planar AdS black holes and to the spectrum around AdS in various cases. Requiring that the dual theory is unitary strongly constrains the higher derivative terms in the action, as the operators associated with the extra boundary conditions generically have complex conformal dimensions and non-positive norms.Comment: 57 pages; v2 - references and comments adde

No abstract

No abstract