Hydrodynamics of R-charged black holes

TL;DR

This work analyzes the hydrodynamics of ${\cal N}=4$ SYM at finite ${\rm R}$-charge densities using the AdS/CFT correspondence, employing the STU black hole as the gravity dual. The authors compute the shear viscosity via Kubo formula in the multi-charge background and show that $\eta/s = 1/(4\pi)$ regardless of the chemical potentials, extending the universality observed at zero density. In the single-charge case they derive the diffusion pole in stress-energy and R-current correlators, obtaining a diffusion constant $\mathcal{D}=\frac{1}{4\pi T_H}\frac{1+\hat{\kappa}/2}{1+\hat{\kappa}}$ consistent with $\eta=(\varepsilon+P)\mathcal{D}$. They also determine the thermal conductivity $\kappa_T$ and reveal a Wiedemann-Franz–like relation $\kappa_T\mu^2/(\eta T_H)=8\pi^2$, along with a critical scaling analysis near the thermodynamic stability boundary, where derivatives of transport coefficients diverge with exponent $1/2$. Together, these results deepen the understanding of holographic hydrodynamics at finite density and reveal robust transport structures across the phase diagram; future work includes the all-three-charge case and exploration of possible phase transitions.

Abstract

We consider hydrodynamics of N=4 supersymmetric SU(N_c) Yang-Mills plasma at a nonzero density of R-charge. In the regime of large N_c and large 't Hooft coupling the gravity dual description involves an asymptotically Anti- de Sitter five-dimensional charged black hole solution of Behrnd, Cvetic and Sabra. We compute the shear viscosity as a function of chemical potentials conjugated to the three U(1) \subset SO(6)_R charges. The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to 1/4π. For a single charge black hole we also compute the thermal conductivity, and investigate the critical behavior of the transport coefficients near the boundary of thermodynamic stability.