A random matrix-like model for the Polyakov loop and center symmetry

TL;DR

This paper introduces a random matrix-like model for the Polyakov loop in SU(N) Yang-Mills theories, capturing phase transition behaviors and center symmetry breaking with analytical insights and comparisons.

Contribution

It presents a novel simplified eigenvalue-based model for the Polyakov loop that reproduces the order of phase transitions in SU(2) and SU(3) Yang-Mills theories.

Findings

Reproduces first-order deconfinement transition for SU(3)

Reproduces second-order transition for SU(2)

Provides analytical phase analysis and comparisons

Abstract

We formulate a random matrix-like model for the Polyakov loop in SU(N) Yang-Mills theories. It describes a simplified dynamics in terms of eigenvalue differences. The deconfinement phase transition encoded in center symmetry breaking is reproduced including its nature being first order for SU(3) and second order for SU(2). Analytical arguments about the phases are presented and a comparison to other approaches is made.