Temperature dependence of topological susceptibility using gradient flow

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.

Comments: 6 pages, 8 figures. Talk presented at the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK