"Confinement Mechanism in Various Abelian Projections of $SU(2)$ Lattice Gluodynamics"

TL;DR

This paper investigates how the monopole confinement mechanism in lattice gluodynamics depends on the choice of abelian projection, showing that confinement can arise from different topological objects depending on the projection used.

Contribution

It provides an explicit example of a non-monopole confinement mechanism in the minimal abelian projection and analyzes the role of the Faddeev--Popov determinant in different projections.

Findings

Confinement in the maximal abelian projection is monopole-driven.

In the minimal abelian projection, confinement arises from other topological objects.

Analytical and numerical analysis of the Faddeev--Popov determinant reveals differences between projections.

Abstract

We show that the monopole confinement mechanism in lattice gluodynamics is a particular feature of the maximal abelian projection. We give an explicit example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We perform analytical and numerical study of the loop expansion of the Faddeev--Popov determinant for the maximal and the minimal abelian projections, and discuss the fundamental modular region for these projections.