Properties of the deconfining phase transition in SU(N) gauge theories

TL;DR

This study investigates the finite-temperature deconfinement transition in SU(N) gauge theories, focusing on the large-N limit and using lattice simulations to quantify the deconfining temperature, latent heat, masses, and string tensions. It demonstrates that for N≥4 the transition is robustly first order with latent heat scaling as $L_h\propto N^2$, while the interface tension grows with N; at high temperature spatial string tensions scale as $T^2$ and K-string tensions follow Casimir scaling. Across N≤8, Tc in units of the string tension approaches a constant with $O(1/N^2)$ corrections, and there is strong evidence against multi-step deconfinement, i.e., a single Tc governs all $k$-strings. The SU(2) case remains second order, with the diverging correlation length visible in Polyakov-loop channels but not in equal-time correlators, highlighting subtleties of interpreting Euclidean finite-temperature results. Overall, the work provides a coherent large-N picture of deconfinement and informs expectations for real-world SU(3) dynamics and possible Master-Field structures at N→∞.

Abstract

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N->oo. We calculate the latent heat in the continuum limit, and find the expected quadratic in N behaviour at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N>3 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T=Tc confirming the discontinuous nature of the transition for N>2. We explicitly show that the large-N `spatial' string tension does not vary with T for T<Tc and that it is discontinuous at T=Tc. For T>Tc it increases as T-squared to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single Tc at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between linear or quadratic in N variations, each of which can lead to a striking but different N=oo deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed.

Figures (14)

• Figure 1: The value of the 't Hooft coupling on the scale $a$, as obtained from $\beta$ in eqn(\ref{['eqn_ggNI']}), for $N=2(\circ),3(\Box),4(\star),6(+),8(\bullet)$, plotted against the values of $a$ expressed in physical units.
• Figure 2: The SU($N$) continuum deconfining temperature in units of the string tension, with an extrapolation to $N=\infty$ using a leading $O(1/N^2)$ correction.
• Figure 3: The latent heat calculated at $a=1/5T_c$ for various SU($N$) groups.
• Figure 4: The deconfining latent heat in SU(4), $\diamond$, SU(6), $\Box$ and SU(8), $\circ$ gauge theories at various $a$, with extrapolations to the continuum limit using a $O(a^2)$ correction.
• Figure 5: The masses of the lightest $k=1$ ($\bullet$) and $k=2$ ($\circ$) flux loops that wind around the time-torus, in the confining phase at $T=T_c$, $a=1/5T_c$ for various SU($N$) gauge theories.