Holographic Hydrodynamics with a Chemical Potential

TL;DR

This work analyzes holographic hydrodynamics of a strongly coupled CFT with a finite chemical potential by extending 5D gravity with a U(1) field to include general four-derivative terms. The authors construct charged planar AdS black holes perturbatively in the four-derivative couplings and compute transport coefficients—most notably the shear-viscosity to entropy-density ratio η/s and the electrical conductivity—within the AdS/CFT framework. They show that μ enhances violations of the KSS bound in many models and that higher-derivative corrections reshape key bounds on conductivity-related ratios, while some results (e.g., entropy) remain tied to Wald-type expressions. The analysis also clarifies how central charges and anomalies in the dual CFT constrain the gravitational couplings, and discusses implications for weak gravity conjecture-inspired consistency checks in holographic theories.

Abstract

We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions perturbatively and consider the thermal and hydrodynamic properties of the plasma in the dual CFT. In particular, we calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential. We also compute the electrical conductivity and comment on various conjectured bounds related to this coefficient.