Do Large Abelian Monopole Loops Survive the Continuum Limit?

Abstract

An analysis of the monopole loop length distribution is performed in Wilson-action SU(2) lattice gauge theory. A pure power law in the inverse length is found, at least for loops of length, $l$, less than the linear lattice size $N$. This power shows a definite $\beta$ dependence, passing 5 around $\beta =2.9$, and appears to have very little finite lattice size dependence. It is shown that when this power exceeds 5, no loops any finite fraction of the lattice size will survive the infinite lattice limit. This is true for any reasonable size distribution for loops larger than N. The apparent lack of finite size dependence in this quantity would seem to indicate that abelian monopole loops large enough to cause confinement do not survive the continuum limit. Indeed they are absent for all $\beta > 2.9$.