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

TL;DR

This paper demonstrates a method to relate Einstein-Maxwell-Dilaton theories to higher-dimensional AdS-Maxwell gravity through generalized dimensional reduction, enabling the derivation of holographic and hydrodynamic properties from simpler models.

Contribution

It introduces a generalized dimensional reduction technique connecting EMD theories to AdS-Maxwell gravity, facilitating analysis of complex black hole solutions and their holographic duals.

Findings

Derived holographic dictionary for EMD theories.

Computed transport coefficients like conductivity and viscosities.

Linked black hole solutions to simpler AdS-Maxwell solutions.

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.