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

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.