Various Abelian Projections of $SU(2)$ Lattice Gluodynamics and Aharonov-Bohm Effect in the Field Theory

TL;DR

This paper investigates how abelian projections in lattice gluodynamics reveal monopoles and strings, which may both contribute to color confinement, supported by explicit results in the Abelian Higgs model.

Contribution

It demonstrates that abelian projections contain both monopoles and strings, suggesting multiple topological excitations could be responsible for confinement.

Findings

Monopoles and strings coexist in abelian projections.

Both excitations may contribute to color confinement.

Explicit results obtained in the Abelian Higgs model support the ideas.

Abstract

We show that in general abelian projection of lattice gluodynamics it is not only monopoles but also strings are present. Both these topological excitations may be responsible for the confinement of color. We illustrate our ideas by some explicit results in the Abelian Higgs model with the Villain action.