Holography and hydrodynamics for EMD theory with two Maxwell fields

Abstract

We use ‘generalized dimensional reduction’ to relate a specific Einstein-Max-well-Dilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higher-dimensional AdS gravity (with no higher-dimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to non-integral values. Specifically, we perform a non-diagonal Kaluza-Klein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the lower-dimensional theory by performing the generalized dimensional reduction on AdS. We study a specific example of a black brane carrying a wave, whose universal sector is described by gravity coupled to two Maxwell fields, three neutral scalars and an axion, and compute the first order transport coefficients of the dual theory. In these theories $ {{\widehat{\zeta}}_s}/\widehat{\eta}<2\left( {1/\left( {d-1} \right)-\widehat{c}_s^2} \right) $ , where $ {{\widehat{c}}_s} $ is the speed of sound, violating a conjectured bound, but an alternative bound is satisfied.