Remarks on correlators of Polyakov Loops

TL;DR

This paper investigates the eigenvalues and correlations of Polyakov loops in 2D and 4D SU(N) Yang-Mills theories, revealing unique correlation structures and discussing potential large-N phase transitions.

Contribution

It provides a detailed analysis of Polyakov loop eigenvalues and their correlations, highlighting differences from random matrix models and exploring conditions for large-N phase transitions.

Findings

Connected correlation function differs from hermitian random matrix ensembles.

No large N non-analyticities found in two-point functions in the confining regime.

Suggestions for potential large-N phase transitions involving Polyakov loops.

Abstract

Polyakov loop eigenvalues and their N-dependence are studied in 2 and 4 dimensional SU(N) YM theory. The connected correlation function of the single eigenvalue distributions of two separated Polyakov loops in 2D YM is calculated and is found to have a structure differing from the one of corresponding hermitian random matrix ensembles. No large $N$ non-analyticities are found for two point functions in the confining regime. Suggestions are made for situations in which large-N phase transitions involving Polyakov loops might occur.