Monopole action and condensation in SU(2) QCD

TL;DR

This paper derives an effective monopole action in SU(2) QCD, showing monopole condensation persists in the infinite-volume limit, independent of lattice volume and coupling parameters.

Contribution

It introduces a volume-independent monopole action derived from vacuum configurations, revealing monopole condensation's universality in lattice QCD.

Findings

Monopole action depends only on physical lattice spacing, not on $eta$.

Entropy dominates monopole loop energy for large lattice spacing.

Monopole condensation occurs in the infinite-volume limit across all $eta$.

Abstract

An effective monopole action for various extended monopoles is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. The action appears to be independent of the lattice volume. Moreover it seems to depend only on the physical lattice spacing of the renormalized lattice, not on $\beta$. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} \Lambda_L^{-1}$. This suggests that monopole condensation always (for all $\beta$) occurs in the infinite-volume limit of lattice QCD.