Polyakov loop renormalization with gradient flow

TL;DR

This paper introduces a gradient flow method for renormalizing Polyakov loops across multiple representations in 2+1 flavor QCD, enabling accurate, low-error results over a wide temperature range.

Contribution

The study presents a novel gradient flow-based renormalization technique for Polyakov loops applicable to various representations in lattice QCD.

Findings

Effective renormalization over 100-800 MeV temperature range.

Small errors achieved for higher representations.

Confirmation of Casimir scaling in Polyakov loops.

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.