# Confinement Mechanism in Various Abelian Projections of Lattice Gluodynamics

## TL;DR

This paper investigates the confinement mechanism in lattice gluodynamics, revealing it may depend on the specific abelian projection used, and identifies alternative topological objects responsible for confinement in certain projections.

## Contribution

It demonstrates that monopole confinement is projection-dependent and provides an example where confinement arises from different topological objects.

## Key findings

- Monopole confinement may be specific to the maximal abelian projection.
- In the minimal abelian projection, confinement is due to other topological objects.
- Discussion of the string representation of abelian projected $SU(2)$ gluodynamics.

## Abstract

We show that the monopole confinement mechanism in lattice gluodynamics may be 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 also discuss the string representation of the abelian projected $SU(2)$ gluodynamics.