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

TL;DR

This work establishes a holographic framework for a broad class of Einstein–Maxwell–dilaton theories by relating them, through generalized dimensional reduction, to higher-dimensional AdS–Maxwell gravity. The authors show that reductions over Einstein manifolds or tori yield lower-dimensional theories with two exponential dilaton potentials or a single exponential, and that many nontrivial black hole and black brane solutions descend from simpler AdS solutions. They develop a holographic dictionary by reducing higher-dimensional AdS counterterms and identify the dual operators and Ward identities, enabling the computation of thermodynamics and universal hydrodynamics in the EMD theories. The results yield universal transport coefficients (e.g., η/s = 1/(4π)) and show how charge and the generalized conformal structure alter bulk viscosity and conductivity, with implications for holographic modeling of finite-density systems. The framework also provides a systematic route to study boosted, charged branes and their hydrodynamics across a continuum of dimensional reductions.

Abstract

We 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.