The high temperature phase transition in SU(N) gauge theories

TL;DR

This paper calculates the deconfining temperature in SU(N) gauge theories for various N, showing its dependence on N, confirming the first-order nature of the phase transition for N ≥ 3, and discussing implications for large-N limits.

Contribution

It provides new continuum values of the deconfining temperature for SU(4), SU(6), and SU(8), and refines the N-dependence fit, confirming the transition's order and volume effects.

Findings

The N-dependence of T_c/√σ fits well to a 1/N^2 expansion.

The phase transition is first order for N ≥ 3 and intensifies with N.

Finite volume effects diminish rapidly as N increases.

Abstract

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the $N$-dependence for $2 \leq N \leq 8$ is well fitted by $T_c/\sqrt{sigma} = 0.596(4) + 0.453(30)/N^2$, showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for $N \geq 3$ and that it becomes stronger with increasing $N$. We also confirm that as $N$ increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with $N$. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.