The dynamics of zero modes in lattice gauge theory - difference between SU(2) and SU(3) in 4D

The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum A mu(x) = 0 due to the existence of nontrivial degenerate vacua known as torons. Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large beta. While we confirm the leading 1/beta predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors.

Automated summary

This article investigates the dynamics of zero modes in gauge theory and reveals the instability between trivial vacuum and nontrivial vacuum in 4D SU(2) and SU(3) theories through Monte Carlo calculations of Wilson loops and Polyakov lines.