Strong-coupling effective action(s) for SU(3) Yang-Mills

TL;DR

This paper develops strong-coupling effective theories for SU(3) Yang-Mills at finite temperature, enabling estimation of phase transition points and validation through Monte Carlo simulations, with corrected group measure calculations.

Contribution

It introduces dimensionally reduced $Z_N$-symmetric effective theories for SU(3) Yang-Mills and provides accurate mappings to estimate critical points, correcting previous group measure errors.

Findings

Effective theories accurately estimate critical points at low $N_\tau$

Monte Carlo simulations show good agreement with original theories

Corrected group measure improves numerical results

Abstract

We apply strong-coupling expansion techniques to finite-temperature lattice pure gauge theory, obtaining dimensionally reduced $Z_N$-symmetric effective theories. The analytic mappings between the effective couplings and the original one, viz. $\beta$, allow to estimate the transition point $\beta_c$ of the 4D theory for a large range of the imaginary-time extent $N_\tau$ of the lattice. We study the models for SU(3) via Monte Carlo simulation, finding satisfactory agreement with the critical point of the original theories especially at low $N_\tau$. We have fixed an error in the group measure used in arXiv:1010.0951 and provide here the correct numerical results.