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

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 $SU(2)\to U(1)$ 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.