Transport in a gravity dual with a varying gravitational coupling constant

TL;DR

This paper investigates how varying gravitational couplings in AdS backgrounds affect transport properties like conductivity and viscosity, revealing deviations from universal bounds and temperature-dependent behaviors in higher dimensions.

Contribution

It introduces models with a varying gravitational coupling in AdS spaces, analyzing their impact on conductivity and viscosity, and explores momentum relaxation effects in different dimensions.

Findings

dc conductivity deviates from universal EMD results

shear viscosity to entropy ratio saturates KSS bound

dc conductivity decreases with temperature in higher dimensions

Abstract

We study asymptotically AdS Brans-Dicke (BD) backgrounds, where the Ricci tensor R is coupled to a scalar in the radial dimension, as effective models of metals with a varying coupling constant. We show that, for translational invariant backgrounds, the regular part of the dc conductivity $\sigma_Q$ deviates from the universal result of Einstein-Maxwell-Dilaton (EMD) models. However, the shear viscosity to entropy ratio saturates the Kovtun-Son-Starinets (KSS) bound. Similar results apply to more general f(R) gravity models. In four bulk dimensions we study momentum relaxation induced by gravitational and electromagnetic axion-dependent couplings. For sufficiently strong momentum dissipation induced by the former, a recently proposed bound on the dc conductivity $\sigma$ is violated for any finite electromagnetic axion coupling. Interestingly, in more than four bulk dimensions, the dc conductivity for strong momentum relaxation decreases with temperature in the low temperature limit. In line with other gravity backgrounds with momentum relaxation, the shear viscosity to entropy ratio is always lower than the KSS bound. The numerical computation of the optical conductivity reveals a linear growth with the frequency in the limit of low temperature, low frequency and large momentum relaxation. We have also shown that the module and argument of the optical conductivity for intermediate frequencies are not consistent with cuprates experimental results, even assuming several channel of momentum relaxation.