Vortex induced confinement and the Kugo-Ojima confinement criterion

TL;DR

This paper investigates the connection between vortex structures and confinement in SU(2) Yang-Mills theory by analyzing gluon and ghost propagators through lattice simulations, confirming the Kugo-Ojima criterion's relevance.

Contribution

It demonstrates that removing confining vortices from lattice ensembles eliminates the ghost propagator divergence, linking vortex presence to confinement and the Kugo-Ojima criterion.

Findings

Ghost propagator divergence is confirmed in confining SU(2) theory.

Removing vortices results in loss of ghost divergence.

Vortex removal correlates with deconfinement evidence.

Abstract

The SU(2) Yang-Mills gluon and ghost Green-functions are studied in Landau gauge by means of lattice gauge simulations. A focal point is their low energy behavior since in particular the Kugo-Ojima confinement criterion relates a diverging ghost form factor at vanishing momentum transfer to the confining capabilities of the theory. This divergence is verified by numerical simulations. Removing the confining vortices from the lattice ensembles converts SU(2) Yang-Mills theory in a non-confining theory. It is shown that in this modified theory the divergence of the ghost propagator disappears.