Higher derivative effects on eta/s at finite chemical potential

TL;DR

Problem: assess how higher-derivative corrections affect the shear viscosity to entropy density ratio in a holographic theory with finite $R$-charge chemical potential. Approach: compute in $D=5$ $\mathcal{N}=2$ gauged supergravity with the four-derivative $A\wedge\mathrm{Tr}(R\wedge R)$ term, derive the corrected $R$-charged black hole background, and evaluate $\eta/s$ via the Kubo formula in the hydrodynamic limit, perturbative in $\bar{c}_2$. Findings: $\eta/s$ deviates from the universal value by $-\bar{c}_2(1+q)$, with $q$ tied to the chemical potential via $\Phi=g r_0\sqrt{3q(1+q)}$ and the anomaly data via $\bar{c}_2=(c-a)/a$; the bound is violated for $c-a>0$, with larger $\Phi$ increasing the violation. Significance: demonstrates that finite-$N$ and finite-chemical-potential effects can produce controlled violations of the KSS bound in a supersymmetric, holographic setting, illuminating the limits and possible universality of the bound in higher-derivative, supersymmetric theories.

Abstract

We examine the effects of higher derivative corrections on eta/s, the ratio of shear viscosity to entropy density, in the case of a finite R-charge chemical potential. In particular, we work in the framework of five-dimensional N =2 gauged supergravity, and include terms up to four derivatives, representing the supersymmetric completion of the Chern-Simons term A \wedge Tr (R \wedge R). The addition of the four-derivative terms yields a correction which is a 1/N effect, and in general gives rise to a violation of the eta/s bound. Furthermore, we find that, once the bound is violated, turning on the chemical potential only leads to an even larger violation of the bound.