Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series

TL;DR

This paper develops improved three-dimensional effective actions for thermal SU(N) Yang-Mills theory using strong coupling expansions, accurately capturing phase transitions and critical couplings for different N_tau values.

Contribution

It extends previous effective actions by including higher order and interaction terms, providing analytic mappings to original lattice parameters, and validates them through Monte Carlo simulations.

Findings

Accurately reproduces second order and first order phase transitions for SU(2) and SU(3).

Calculates critical couplings with few percent accuracy for N_tau=4-16.

Provides a systematic method to connect effective theory parameters with original lattice parameters.

Abstract

We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters $N_\tau,\beta$ of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings $\beta_c(N_\tau)$ and find agreement with results from simulations of the 4d theory at the few percent level for $N_\tau=4-16$.