1209.0260 (Kiminad A. Mamo)

Violation of the Holographic Shear Viscosity Bound in Strongly Coupled
Isotropic Plasmas with Einstein Gravity Dual    [PDF]

Kiminad A. Mamo

We revisit the AdS/CFT calculations of the shear viscosity of isotropic, strongly coupled quark gluon plasmas with Einstein gravity dual by emphasizing the fact, which was overlooked in the previous literatures, that the shear viscosity is a fourth-rank tensor. First, we show that since the shear viscosity tensor has to be regular at the horizon, its indices should be raised and lowered by using the metric components evaluated at the horizon. Then, we find that indeed the holographic (Kovtun-Son-Starinets) shear viscosity bound is saturated by the 'two indices up and two indices down' shear viscosity tensor to entropy density ratio \frac{\eta^{j}_{i}^{j}_{i}}{s} but it is violated by both the 'four indices down' \frac{\eta_{jiji}}{s} and the 'four indices up' \frac{\eta^{jiji}}{s}. Specifically, for the isotropic, strongly coupled N=4 super-Yang-Mills plasma with Einstein gravity dual, we find that \frac{\eta_{jiji}}{s}=1/4\pi^3 T^4, and \frac{\eta^{jiji}}{s}=\frac{1}{4\pi^5 T^4}.

View original: http://arxiv.org/abs/1209.0260