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

TL;DR

This paper uses a gravity dual model to accurately describe the equation of state and viscosities of the gluon plasma, matching recent lattice data and providing insights into non-conformal effects.

Contribution

It introduces a bottom-up gravity dual model calibrated with new lattice data to compute the gluon plasma's equation of state and viscosity ratios, revealing non-conformal behavior.

Findings

The bulk-to-shear viscosity ratio follows a specific relation with non-conformality.

The shear viscosity to entropy density ratio remains at the universal value (1/4π).

Maximum bulk viscosity ratio reaches 0.94 at a certain non-conformality measure.

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.