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

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 230Tc with Tc 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 Tc the results exhibit a striking linear behaviour in ln⁡(T/Tc)−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 Ts=(ϵ+p). The continuum values of the potentials are well represented by Padé 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 Tc is analyzed and resolved thanks to the high precision achieved.