Confined-deconfined interface tension and latent heat in SU(N) gauge theory

TL;DR

This study delivers high-precision lattice determinations of the confined-deconfined interface tension and latent heat for SU($N$) gauge theories with $N=4,5,8,10$, confirming leading $O(N^2)$ scaling and quantifying subleading corrections. The mixed-phase ensemble, combined with capillary-wave theory, enables direct extraction of $eta_c$, $\sigma$, and $L$ while avoiding supercritical slowing down; kernel-corrected spectra are used to extrapolate to the long-wavelength limit. The continuum and large-$N$ analyses yield the robust large-$N$ limits $ frac{\sigma}{T_c^3} = 0.0182(7)\,N^2 - 0.194(15)$ and $ frac{L}{T_c^4} = 0.360(6)\,N^2 - 1.88(17)$, with detailed treatment of lattice beta functions. These precise results inform the thermodynamics of large-$N$ gauge theories and have potential implications for cosmology and gravitational-wave phenomenology in dark SU($N$) sectors.

Abstract

We present high-precision lattice results for the confined-deconfined interface tension and the latent heat of pure SU($N$) gauge theories up to $N=10$ and investigate their asymptotic $N$-dependency. For both quantities we observe the leading $N^2$ behaviour and subleading corrections, with the result for the interface tension $σ/T_c^3 = 0.0182(7) N^2 - 0.194(15)$ and for the latent heat $L/T_c^4 = 0.360(6) N^2 - 1.88(17)$. We use the \emph{mixed phase ensemble} method - where the system is constrained so that half of the volume is in the confined phase and the other half in the deconfined phase - and the interface tension is obtained by measuring the capillary wave fluctuation spectra of the interfaces between the two phases. The method bypasses supercritical slowing down from which other methods for determining the interface tension suffer, and as a by-product produces accurate estimates of the critical inverse gauge coupling as a function of the inverse temperature. We use the latter to determine the lattice beta function values, required to compute the latent heat from the discontinuity in the average plaquette action across the confined-deconfined transition.

Figures (11)

• Figure 1: Schematic real part of the Polyakov line $\mathrm{Re\,} P_L$ distribution at $\beta_c$ (dashed curve), with restriction to the central region (red lines).
• Figure 2: Two-phase configuration with two planar interfaces corresponding to the central region of $\mathrm{Re\,} P_L$ distribution in Fig. \ref{['fig:schematic']}.
• Figure 3: Top row: Schematics of how the order parameter probability distribution is expected to look globally and restricted to a small interval at the center of the distribution (marked by the vertical red lines) at values of the inverse gauge coupling $\beta$ slightly below (left), equal to (center), and slightly above (right) its pseudo critical value $\beta_c$. Bottom row: Measured probability distributions of the real part of the Polyakov line $\mathrm{Re\,} P_L$ of SU(8) gauge theory on a $6\times 50^2 \times 160$ lattice slightly below, at, and above the critical $\beta$. In the simulation $\mathrm{Re\,} P_L$ was restricted to range $0.1805 \le \mathrm{Re\,} P_L \le 0.1845$.
• Figure 4: Volume dependence of the critical coupling $\beta_c$ on SU(8), $N_t=6$ lattices.
• Figure 5: Capturing the confined-deconfined interface from a configuration in coexisting-phase-restricted simulation of SU(8) gauge theory on a $80^2\times 240\times 6$ lattice at $\beta=44.56196$. Left column: real trace of Polyakov loop in the $x$-$z$-plane at $y=40$ after $n_s=$10 (top), 20 (middle), and 60 (bottom) repeated convolutions with the smearing kernel from Eq. \ref{['eq:smearingkernel']}. The red lines mark the detected phase boundaries in the $x$-$z$-plane at $y=40$, based on the chosen deconfined threshold value for the Polyakov loop. Right column: phase boundary surfaces obtained by performing the deconfined threshold value detection in the Polyakov loop field over the whole spatial volume instead of over a slice of constant $y$ coordinate. The red lines are the same as in the corresponding panels in left column. After 10 smearing steps, UV noise in the local Polyakov loop observable is still significant and prevents a unique detection of the $x$-$y$-spanning phase boundaries. With increasing numbers of smearing steps, the noise gradually disappears and the two $x$-$y$-spanning phase boundaries can be uniquely mapped out and parametrized as functions $z_{i}\mathopen{}\mathclose{\left(x,y\right)$, $i=1,2$.