Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory

TL;DR

This paper investigates holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory, deriving analytical and numerical results for conductivity and diffusion constants in a charged black brane background.

Contribution

It introduces a method to compute transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory, accounting for the mixing of Gauss-Bonnet and Maxwell fields, and derives their dependence on cutoff surface position.

Findings

AC conductivity matches numerical results at low frequency

DC conductivity exhibits radial flow influenced by Gauss-Bonnet coupling

Diffusion constant depends on Gauss-Bonnet coupling and cutoff surface location

Abstract

We apply the membrane paradigm and the holographic Wilsonian approach to the Einstein-Gauss-Bonnet-Maxwell theory. The transport coefficients for a quark-gluon plasma living on the cutoff surface are derived in a spacetime of charged black brane. Because of the mixing of the Gauss-Bonnet coupling and the Maxwell fields, the vector modes/shear modes of the metric and Maxwell fluctuations turn out to be very difficult to decouple. We firstly evaluate the AC conductivity at a finite cutoff surface by solving the equation of motion numerically, then manage to derive the radial flow of DC conductivity with the use of the Kubo formula. It turns out that our analytical results match the numerical data in low frequency limit very well. The diffusion constant $D(u_c)$ is also derived in a long wavelength expansion limit. We find it depends on the Gauss-Bonnet coupling as well as the position of the cutoff surface.