Equation of state of a relativistic theory from a moving frame

Abstract

We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to compute the expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor in presence of shifted boundary conditions. The entropy is thus easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9 T_c - 20 T_c. At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a byproduct we also determine the ultraviolet finite renormalization constant of T_{0k} by imposing suitable Ward identities. These findings establish this strategy as a solid, simple and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.

arXiv comment4 pages, 4 figures

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• Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
• QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
• High-Temperature QCD: theory overview
• Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
• Jarzynski's theorem for lattice gauge theory
• Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
• Lattice QCD at nonzero temperature and density
• Fixed-scale approach to finite-temperature lattice QCD with shifted boundaries
• Non-perturbative renormalization of the QCD flavour-singlet local vector current
• $t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor
• The energy-momentum tensor in lattice QCD and the Equation of State