Renormalization of the Polyakov loop with gradient flow

TL;DR

This paper introduces a gradient flow method to renormalize the Polyakov loop across various representations in 2+1 flavor QCD, enabling precise calculations over a wide temperature range and comparing with existing schemes.

Contribution

The study applies gradient flow for Polyakov loop renormalization in multiple representations, providing high-precision results over a broad temperature spectrum in lattice QCD.

Findings

Successful renormalization of Polyakov loops in multiple representations.

Polyakov loops exhibit Casimir scaling behavior.

Results agree with standard renormalization methods.

Abstract

We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2+1 flavor QCD with highly improved staggered quarks and lattices with temporal extents of $N_\tau=6$, $8$, $10$ and $12$ we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from $T=116$ MeV up to $T=815$ MeV, with small errors not only for the Polyakov loop in fundamental representation, but also for the Polyakov loops in higher representations. We compare our results with standard renormalization schemes and discuss the Casimir scaling of the Polyakov loops.