Temperature dependence of topological susceptibility using gradient flow

TL;DR

This study investigates how the topological susceptibility in QCD varies with temperature, comparing different measurement methods and confirming the dilute instanton gas approximation's prediction at low temperatures.

Contribution

It demonstrates the agreement between gluonic and fermionic definitions of topological susceptibility using gradient flow and verifies the dilute instanton gas approximation at low temperatures.

Findings

Good agreement between gluonic and fermionic susceptibility measurements.

Confirmation of the power-law decay of susceptibility as (T/T_{pc})^{-8}.

Validation of the dilute instanton gas approximation prediction.

Abstract

We study temperature dependence of the topological susceptibility with the $N_{f}=2+1$ flavors Wilson fermion. We have two major interests in this paper. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Two definitions are related by the chiral Ward-Takahashi identity but their coincidence is highly non-trivial for the Wilson fermion. By applying the gradient flow both for the gauge and quark fields we find a good agreement of these two measurements. The other is a verification of a prediction of the dilute instanton gas approximation at low temperature region $T_{pc}< T<1.5T_{pc}$, for which we confirm the prediction that the topological susceptibility decays with power $\chi_{t}\propto(T/T_{pc})^{-8}$ for three flavors QCD.