Confinement in $QCD$: novelties

TL;DR

This paper advances understanding of quark confinement in QCD by constructing a gauge-invariant monopole creation operator, providing an order parameter that distinguishes confined and deconfined phases, and explaining flux tube properties.

Contribution

It introduces a gauge-invariant monopole creation operator as an order parameter for confinement in QCD, addressing previous issues of gauge dependence and infrared divergences.

Findings

Order parameter is gauge-invariant and finite in the confined phase.

Flux tubes do not retain memory of monopole color orientation.

Order parameter relates to the vacuum correlator of the chromo-electric field.

Abstract

We report on recent progress in understanding confinement of colour in $QCD$ as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order parameter. This order parameter is gauge-invariant from scratch, has no infrared divergences, is finite in the confined phase and vanishes in the deconfined phase. A natural explanation also emerges of why the electric field lines in the flux tubes keep no memory of the colour orientation of the condensing monopoles. A further by-product is that the order parameter can be traded with the two-point vacuum parallel correlator of the chromo-electric field.