Temperature dependence of topological susceptibility using gradient flow

We study temperature dependence of the topological susceptibility with the Nf = 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 χτ ∝ (T/Tpc)^-8 for three flavors QCD.