Equation of State and Viscosities from a Gravity Dual of the Gluon Plasma

Abstract

Employing new precision data of the equation of state of the SU(3) Yang-Mills theory (gluon plasma) the dilaton potential of a gravity-dual model is adjusted in the temperature range $(1 - 10) T_c$ within a bottom-up approach. The ratio of bulk viscosity to shear viscosity follows then as $\zeta/\eta \approx \pi \Delta v_s^2$ for $\Delta v_s^2 < 0.2$ and achieves a maximum value of $0.94$ at $\Delta v_s^2 \approx 0.3$, where $\Delta v_s^2 \equiv 1/3 - v_s^2$ is the non-conformality measure and $v_s^2$ is the velocity of sound squared, while the ratio of shear viscosity to entropy density is known as $(4 \pi)^{-1}$ for the considered set-up with Hilbert action on the gravity side.