Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow

TL;DR

This paper presents a lattice QCD study of the equation of state for SU(3) gauge theory at finite temperature using the gradient flow method to measure the energy-momentum tensor, achieving high precision results.

Contribution

It introduces a direct lattice measurement technique for the energy-momentum tensor via gradient flow, providing an alternative to the integral method with comparable accuracy.

Findings

Thermodynamic quantities are obtained with a few percent precision.

Results agree well with previous high-precision data from the integral method.

The study demonstrates the effectiveness of the gradient flow approach for thermodynamic measurements.

Abstract

The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $\beta=6.287$--$7.500$ corresponding to the lattice spacing $a= 0.013$--$0.061\,\mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s= 64$, $96$, $128$ ($N_{\tau}=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33 \le N_s/N_{\tau} \le 8$. Double extrapolation, $a\rightarrow 0$ (the continuum limit) followed by $t\rightarrow 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.