Monopole fields from vortex sheets reconciling Abelian and center dominance

TL;DR

This paper introduces a novel order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory, linking magnetic monopoles and center vortices while resolving previous inconsistencies.

Contribution

It presents a new monopole field correlator based on vortex sheets that unifies abelian and center dominance in gauge theories.

Findings

Establishes a link between abelian and center dominance.

Resolves inconsistencies in monopole field definitions.

Provides a new order parameter for phase transition.

Abstract

We describe a new order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of magnetic monopole field correlators represented as sums over sheets of center vortices. Our construction establishes a link between "abelian" and "center dominance". It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for magnetic fluxes.