Polyakov loop renormalization with gradient flow

Abstract

We propose to use the gradient flow for the renormalization of Polyakov loops in various representations. We study Polyakov loops in 2+1 flavor QCD using the HISQ action and lattices with temporal extents $N_\tau$=6, 8, 10 and 12 in various representations, including fundamental, sextet, adjoint, decuplet, 15-plet and 27-plet. This alternative renormalization procedure allows for the renormalization over a large temperature range from $T$=100 MeV - 800 MeV, with small errors not only for the fundamental, but also for the higher representations of the Polyakov loop. We discuss the results of this procedure and Casimir scaling of the Polyakov loop.