The deconfinement transition in SU(N) gauge theories

TL;DR

The paper analyzes the deconfinement transition in SU($4$) and SU($6$) gauge theories using finite-temperature lattice simulations to determine the order of the transition in the large-$N$ limit and to estimate the continuum ratio $T_c/\sqrt{\sigma}$. By examining the Polyakov loop and its susceptibility across volumes and lattice spacings, the authors demonstrate a clear, normal first-order transition in both SU($4$) and SU($6$), with finite-volume scaling supporting a non-vanishing latent heat and tunnelling between phases. Continuum extrapolations show only weak $N$-dependence in $T_c/\sqrt{\sigma}$ across SU(2), SU(3), SU($4$), and SU($6$), consistent with a smooth large-$N$ limit where the transition remains first order. The results bolster the large-$N$ picture of QCD-like theories and provide groundwork for related quantities such as topology and k-string tensions near $T_c$.

Abstract

We investigate the properties of the deconfinement transition in SU(4) and SU(6) gauge theories. We find that it is a `normal' first order transition in both cases, from which we conclude that the transition is first order in the N->infinity limit. Comparing our preliminary estimates of the continuum values of Tc/sqrt(K) with existing values for SU(2) and SU(3) demonstrates a weak dependence on N for all values of N.

Figures (8)

• Figure 1: The modulus of the average value of the Polyakov loop for a sequence of $14^3 5$ (top) and $20^3 5$ (bottom) field configurations at $\beta=10.635$ in SU(4).
• Figure 2: A histogram of the values of the average plaquette, for the $20^3 5$ lattice at $\beta_c$ in SU(4).
• Figure 3: The critical value of $\beta$ plotted against the inverse spatial volume, $V$, expressed in units of the temperature, $T$. On $L^3 5$ lattices in SU(4). The straight lines are the extrapolations to infinite volume, one excluding the $L=12$ value. The corresponding extrapolated values are shown slightly to the left of $1/V=0$.
• Figure 4: The specific heat at the critical value of $\beta$, $C(\beta_c,V)$, normalised to the spatial volume $V$ and plotted against $1/V$, with $V$ in units of $T$. The intercept ($\bullet$) at $V=\infty$ provides a measure of the latent heat. For SU(4) and $L_t=5$.
• Figure 5: The difference of the average plaquette in the confining and deconfining phases on $L^3 5$ SU(4) lattices plotted versus $L$. For $\beta=10.635$ ($\circ$) and $\beta=10.637$ ($\bullet$).