Confinement and monopole condensation: some properties of the disorder parameter

TL;DR

This paper shows that the disorder parameter for detecting dual superconductivity in QCD is a gauge-invariant operator, and discusses the effects of abelian projection on the lattice up to lattice spacing corrections.

Contribution

It establishes the disorder parameter as a gauge-invariant operator and analyzes the abelian projection's dependence on lattice spacing in QCD.

Findings

Disorder parameter <μ> is gauge-invariant and detects dual superconductivity.

Abelian projection on the lattice is determined up to O(a^2) corrections.

Provides insight into the properties of the disorder parameter in confining QCD phases.

Abstract

We demonstrate that the disorder parameter $<\mu>$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $\mu$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).