Universality check of Abelian monopoles

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 (TI) tree level 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 $0.06\text{ }\text{ }\mathrm{fm}<a<0.35\text{ }\text{ }\mathrm{fm}$. These results show that the ratio is between 0.90 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.