Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity

TL;DR

This paper uses AdS/CFT correspondence to analyze how Gauss-Bonnet gravity influences hydrodynamics with conserved currents, revealing effects on transport coefficients and the ratio η/s, including magnetic and vortical effects.

Contribution

It provides a first-order perturbative solution in Maxwell-Gauss-Bonnet gravity and explores the impact on dual conformal fluid properties, including transport coefficients and anomalous effects.

Findings

Gauss-Bonnet term affects shear viscosity, entropy density, thermal and electrical conductivities.

The ratio η/s is modified by the Gauss-Bonnet term and bulk Maxwell field.

The Wiedemann-Franz law remains unaffected by the Gauss-Bonnet term.

Abstract

Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity $\eta$, entropy density $s$, thermal conductivity $\kappa$ and electrical conductivity $\sigma$. However, it does not affect the so-called Wiedemann-Franz law which relates $\kappa$ to $\sigma$, while it affects the ratio $\eta/s$. In addition, another interesting result is that the $\eta/s$ can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.