Universality check of Abelian Monopoles

TL;DR

This study investigates the universality of Abelian monopole dominance in SU(2) lattice gauge theory using improved actions, finding consistent monopole density ratios across lattice spacings and gauge choices, with implications for continuum limit behavior.

Contribution

It demonstrates the finite continuum limit of monopole densities with improved actions and compares monopole properties in different gauges, advancing understanding of Abelian dominance universality.

Findings

Monopole density in the IR cluster is finite in the continuum limit.

The ratio of Abelian to non-Abelian string tension remains between 0.9 and 0.95 across lattice spacings.

Infrared monopole properties converge in MAG but not clearly in LAG.

Abstract

We study the Abelian projected SU(2) lattice gauge theory after gauge fixing to the maximally Abelian gauge (MAG). In order to check the universality of the Abelian dominance we employ the tadpole improved tree level (TI) action. We show that the density of monopoles in the largest cluster (the IR component) is finite in the continuum limit which is approximated already at relatively large lattice spacing. The value itself is smaller than in the case of Wilson action. We present results for the ratio of the Abelian to non-Abelian string tension for both Wilson and TI actions for a number of lattice spacings in the range 0.06 fm < a < 0.35 fm. These results show that the ratio is between 0.9 and 0.95 for all considered values of lattice couplings and both actions. We compare the properties of the monopole clusters in two gauges - in MAG and in the Laplacian Abelian gauge (LAG). Whereas in MAG the infrared component of the monopole density shows a good convergence to the continuum limit, we find that in LAG it is even not clear whether a finite limit exists.