Thermodynamics for SU(2) pure gauge theory using gradient flow

TL;DR

This paper computes the scale-setting function and equation of state for pure SU(2) gauge theory using the gradient flow method, introducing a new reference scale t0 and analyzing thermodynamic properties.

Contribution

It introduces a new reference scale t0 for SU(2) gauge theory and applies the gradient flow method to determine thermodynamic quantities.

Findings

Defined a new scale t0 for SU(2) gauge theory.

Calculated thermodynamic quantities as functions of T/Tc.

Demonstrated the use of gradient flow for thermodynamics in SU(2).

Abstract

We present the scale-setting function and the equation of state of the pure SU(2) gauge theory using the gradient flow method. We propose a reference scale t0 for the SU(2) gauge theory satisfying $t^2\langle E \rangle|_{t=t_0} = 0.1$. This reference value is fixed by a natural scaling-down of the standard t0-scale for the SU(3) gauge theory based on the perturbative analyses. We also show the thermodynamic quantities as a function of $T/T_c$, which are derived by the energy-momentum tensor using the small flow time expansion of the gradient flow.