SU(N) Gauge Theories Near $T_c$

TL;DR

This study investigates the deconfinement phase transition in SU(N) gauge theories for N=2,3,4,6,8, revealing a first-order transition that intensifies with N and approaches a large N limit, with implications for the nature of the transition at infinite N.

Contribution

The paper provides a detailed analysis of the N-dependence of the deconfinement transition and its continuum limit behavior, highlighting the large N reduction and the increasing surface tension.

Findings

Transition is first order for N ≥ 3

Rapid approach of T_c/√σ to large N limit

Finite volume effects diminish as N increases

Abstract

We study the deconfinement phase transition in SU(N) gauge theories for $N$=2,3,4,6,8. The transition is first order for $N \ge 3$, with the strength increasing as $N$ increases. We extrapolate $T_c/\sqrt{\sigma}$ to the continuum limit for each $N$, and observe a rapid approach to the large $N$ limit. As $N$ increases the phase transition becomes clear-cut on smaller spatial volumes, indicating the absence of (non-singular) finite volume corrections at $N=\infty$ -- reminiscent of large $N$ reduction. The observed rapid increase of the inter-phase surface tension with $N$ may indicate that for $N=\infty$ the deconfinement transition cannot, in practise, occur.