Phenomenological Equations of State for SU(N) Gauge Theories

TL;DR

This paper introduces two phenomenological models for SU(N) gluon plasmas using Polyakov loop eigenvalues, capturing deconfinement transition behaviors consistent with lattice simulations across various N and temperature ranges.

Contribution

The paper presents two new models with a single free parameter that describe SU(N) gauge theories' thermodynamics and phase transitions, including large-N behavior and eigenvalue dynamics.

Findings

Models match lattice data from T_d to 5T_d

Second order transition for N=2, first order for N=3,4,5

Eigenvalue repulsion characterizes the confined phase

Abstract

Two phenomenological models describing an SU(N) gluon plasma are presented using the eigenvalues of the Polyakov loop as the order parameters of the deconfinement transition. Each model has a single free parameter and exhibits behavior similar to lattice simulations over the range T_d-5T_d. The N=2 deconfinement transition is second order in both models, while N=3,4, and 5 are first order. Both models appear to have a smooth large-N limit. The confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. The motion of the eigenvalues is responsible for the approach to the blackbody limit over the range T_d-5T_d.