An Order Parameter Reconciling Abelian and Center Dominance in SU(2) Yang-Mills Theory

TL;DR

This paper introduces a new order parameter for the confinement-deconfinement transition in SU(2) Yang-Mills theory that resolves previous inconsistencies and unifies abelian and center dominance perspectives.

Contribution

It proposes a novel, gauge-independent order parameter based on regular monopoles and center vortices, improving the understanding of confinement mechanisms.

Findings

The new order parameter avoids flux quantization issues.

It is gauge-independent and consistent across abelian projections.

It links monopole and vortex approaches to confinement.

Abstract

We analyze previously proposed order parameters for the confinement - deconfinement transition in lattice SU(2) Yang-Mills theory, defined as vacuum expectation value (v.e.v.) of monopole fields in abelian projection gauges. We show that they exhibit some inconsistency in the treatment of small scales, due to a violation of Dirac quantization condition for fluxes. We propose a new order parameter avoiding this inconsistency. It can be interpreted as v.e.v. of the field of a regular monopole in any abelian projection gauge, but it is independent of the choice of the abelian projection. Furthermore, being constructed in terms of surfaces of center vortices, it has also a natural interpretation in the approach of center dominance.