Center clusters in the Yang-Mills vacuum

TL;DR

This paper investigates the structure of the Yang-Mills vacuum by analyzing center clusters formed by local Polyakov loops, revealing their role in the deconfinement transition and their continuum limit behavior.

Contribution

It introduces a method to identify and analyze center clusters in the Yang-Mills vacuum, linking cluster percolation to deconfinement transition in lattice gauge theories.

Findings

Center clusters are identified where local Polyakov loops are near the same center element.

Deconfinement transition correlates with the percolation of a specific center sector.

Center clusters exhibit a continuum limit across different lattice resolutions.

Abstract

Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory at finite temperature are analyzed. We show that spatial clusters can be identified where the local Polyakov loops have values close to the same center element. For a suitable definition of these clusters the deconfinement transition can be characterized by the onset of percolation in one of the center sectors. The analysis is repeated for different resolution scales of the lattice and we argue that the center clusters have a continuum limit.