Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame

TL;DR

This paper precisely determines the equation of state of SU(3) Yang-Mills theory in the deconfined phase using lattice simulations with shifted boundary conditions, revealing linear behavior in temperature and resolving previous discrepancies.

Contribution

The study provides a high-precision continuum determination of thermodynamic quantities in SU(3) Yang-Mills theory up to 230 T_c using novel shifted boundary conditions.

Findings

Entropy density exhibits linear behavior in ln(T/T_c)^{-1} over two orders of magnitude.

Results align with Stefan-Boltzmann limit but with a different slope than perturbative predictions.

High-precision data resolve discrepancies in previous near T_c computations.

Abstract

The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\epsilon + p )$. The continuum values of the potentials are well represented by Pad\'e interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near $T_c$ is analyzed and resolved thanks to the high precision achieved.