Confinement-deconfinement order parameter and Dirac's quantization condition

TL;DR

This paper introduces a monopole-like order parameter for the confinement-deconfinement transition in gauge theories, ensuring consistency with Dirac's quantization and applicable to SU(2) lattice Yang-Mills theory.

Contribution

It proposes a new order parameter that respects Dirac's quantization, addressing inconsistencies in previous monopole field definitions in gauge theories.

Findings

The order parameter avoids small-scale inconsistencies.

It aligns with the 't Hooft confinement scenario.

Application to SU(2) lattice Yang-Mills theory outlined.

Abstract

We describe a monopole-like order parameter for the confinement-deconfinement transition in gauge theories where dynamical charges and monopoles coexist. It has been recently proposed in a collaboration with J. Froehlich. It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for electromagnetic fluxes. An application to SU(2) lattice Yang-Mills theory is outlined, naturally fitting in the 't Hooft scenario for confinement.