Shear viscosity from R-charged AdS black holes
J. Mas
TL;DR
The paper computes the holographic shear viscosity in a finite-temperature gauge theory with chemical potential using the STU black hole in AdS$_5$. Employing the Kubo relation and holographic renormalization, it shows that the ratio $\eta/s$ remains the universal value $\frac{1}{4\pi}$ despite nonzero charges, validating universality beyond simple AdS backgrounds. The analysis also highlights the coupling between shear metric perturbations and gauge fields in the STU setup, explaining why naive membrane-paradigm formulas do not trivially apply. Overall, the results reinforce the robustness of the holographic viscosity bound while clarifying how charge interactions impact shear transport in holographic plasmas.
Abstract
We compute the shear viscosity in the supersymmetric Yang-Mills theory dual to the STU background. This is a thermal gauge theory with a chemical potential. The quotient of the shear viscosity over the entropy density exhibits no deviation from the well known result 1/4π.