Holographic Charged Transport with Higher Derivatives

TL;DR

This work extends holographic hydrodynamics to charged plasmas with higher-derivative gravitational corrections, introducing a horizon-based, membrane-paradigm framework that expresses $η$, $ζ$, and $σ$ entirely in terms of black-brane horizon data. By incorporating a bulk $U(1)$ gauge field and scalar-dependent couplings, the authors present two bottom-up models: Model I with perturbative four-derivative corrections and Model II with finite Gauss–Bonnet terms plus perturbative corrections, deriving explicit horizon formulas for all first-order transport coefficients. The results enable systematic exploration of charged transport along holographic RG flows and show how nonconformality and higher-derivative terms shape the temperature and chemical potential dependence of viscosities and conductivity. This horizon-centric approach offers a computationally efficient route to modeling the quark–gluon plasma and other strongly coupled systems in regimes where weak-coupling methods fail, with potential guidance for phenomenology and lattice comparisons.

Abstract

We compute the first-order hydrodynamic transport coefficients (shear viscosity $η$, bulk viscosity $ζ$, and charge conductivity $σ$) for a broad class of strongly coupled, four-dimensional charged relativistic gauge theory plasma with holographic gravitational duals containing higher-derivative corrections. The landscape of our holographic models captures non-conformal gauge theories with an arbitrary number of relevant coupling constants and a general scalar potential in the gravitational dual, allowing for a systematic exploration of charged transport along generic holographic RG flows. The leading-order higher-derivative corrections probe gauge theories with non-equal central charges $c\ne a$ at the ultraviolet fixed point, and enable the engineering of diverse temperature and charge density profiles for the viscosities and the conductivity. Our results establish the membrane paradigm in higher-derivative holographic models: all the transport coefficients are extracted from the black brane horizon values of the gravitational scalars, and various functions defining the gravitational holographic dual.

Figures (1)

• Figure 1: The ratio $R$ of the bulk viscosity to the shear viscosity in the charged hQGP of Buchel:2010gd, see \ref{['deflab']}, as a function of $\frac{\mu}{2\pi T}$. The red dot represents the computation in Buchel:2010gd, at the critical temperature \ref{['tmuabc']}.