Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction

Abstract

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

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

“…Motivated by the above diverse considerations, we would like to make progress on the front of exact black hole solutions in higher-derivative theories. As we shall see, the key in obtaining these combines two ingredients: Lovelock theory and generalised (Kaluza-Klein) dimensional reduction, [54,102,103].…”

“…This explains their scaling behavior as well as the special values of the dilaton functions that separate gapless from gapped solutions. In [103], the effect of non-diagonal KK vectors was investigated.…”

“…By exchanging n -the arbitrary integer number of reduced dimensions -for δ and analytically continuing the latter to the whole real line, this reduction is generalised in the manner of [102,103]. This analytic continuation is possible if and only if one shows the consistency of the KK reduction for an arbitrary number of dimensions, i.e.…”

“…This can be interpreted in the Einstein limit α r = 0 as the fact that the uplifted solution can be either an AdS black hole (λ > 0) or an AdS×H spacetime (λ < 0), [103]. Although this does not happen when the Gauss-Bonnet term is turned on, this interplay of asymptotes still occurs.…”

“…For simplicity, we restrict the discussion to toroidal reductions and flat boundaries. The derivation of the lower-dimensional dictionary via generalised dimensional reduction is explained in full detail in [102,103], so we just sketch it here (see also the review [123]). …”