Colour confinement and gauge-invariant field-strength correlations

TL;DR

This paper provides evidence that colour confinement in QCD results from dual superconductivity of the vacuum, using gauge-invariant field-strength correlations and monopole creation operators to analyze phase transitions.

Contribution

It introduces a gauge-invariant disorder parameter based on field-strength correlations to demonstrate dual superconductivity as the mechanism for confinement in QCD.

Findings

Confinement correlates with non-zero monopole disorder parameter in the confined phase.

Gauge-invariant field strengths are essential for consistent correlation analyses.

The approach resolves the inconsistency regarding the orientation of chromo-electric fields in flux tubes.

Abstract

In this paper we produce evidence that confinement of colour is due to dual superconductivity of $QCD$ vacuum. To do that we put together results of old numerical simulations and results of more recent investigations. The starting point is the expectation that gauge theories admit a dual description in terms of monopoles. The strategy is then to construct the creation operator $\mu$ of a monopole and to compute its vacuum expectation value $\langle \mu \rangle$ , the disorder parameter which indicates dual superconductivity. The Imechanism of confinement is dual superconductivity of vacuum if $\langle \mu \rangle \neq 0 $ in the confined phase , and $\langle \mu \rangle =0$ in the deconfined phase. Confinement has to be certified by independent methods. It is shown that gauge invariance requires that field strengths be replaced by gauge invariant field strengths, which are their parallel transports to infinity. The resulting disorder parameter is a sum of correlation functions of gauge invariant field strength, and its behaviour understood by use of existing lattice data of two-point gauge invariant correlations. As a byproduct an apparent existing inconsistency, the lack of preferred orientation in colour space of the chromo-electric field inside confining flux tubes, is resolved.