SU(N_c) gauge theories at deconfinement

TL;DR

This paper investigates the deconfinement transition in SU(N_c) gauge theories using lattice Monte Carlo simulations, providing refined continuum and large-N_c extrapolations of the critical temperature to string tension ratio.

Contribution

The study offers new high-precision lattice results for N_c=4 to 8, including N_c=5 and 7, with improved control over systematic errors and continuum limit extrapolations, extending understanding of SU(N_c) gauge theories.

Findings

The ratio T_c/√σ fits the formula 0.5949(17)+0.458(18)/N_c^2.

Results are consistent with large-N_c predictions.

Systematic errors are analyzed and discussed.

Abstract

The deconfinement transition in SU($N_c$) Yang--Mills is investigated by Monte Carlo simulations of the gauge theory discretized on a spacetime lattice. We present new results for $ 4 \le N_c \le 8$ (in particular, for $N_c = 5$ and $N_c = 7$), which are analysed together with previously published results. The increased amount of data, the improved statistics and simulations closer to the continuum limit provide us with better control over systematic errors. After performing the thermodynamic limit, numerical results for the ratio of the critical temperature $T_c$ over the square root of the string tension $\sqrt{\sigma}$ obtained on lattices with temporal extensions $N_t = 5,6,7,8$ are extrapolated to the continuum limit. The continuum results at fixed $N_c$ are then extrapolated to $N_c = \infty$. We find that our data are accurately described by the formula $T_c/\sqrt{\sigma} = 0.5949(17) + 0.458(18)/N_c^2$. Possible systematic errors affecting our calculations are also discussed.