Colour confinement and gauge-invariant field-strength correlations

TL;DR

This work provides a gauge-invariant formulation of color confinement as dual superconductivity by constructing a monopole-creation operator $\mu$ and evaluating its disorder parameter $\langle \mu \rangle$. The authors show that, after replacing field strengths with gauge-invariant $F_{\mu\nu}$ via parallel transport to spatial infinity, $\langle \mu \rangle$ can be expressed as a sum of gauge-invariant correlators, with the leading contribution from the two-point chromoelectric-field correlator. In the confined phase, a finite mass gap ensures a finite disorder parameter, while in the deconfined phase the parameter vanishes in the thermodynamic limit, consistent with confinement being tied to monopole condensation. The approach resolves earlier issues related to gauge invariance and flux-tube orientation by grounding the construction in parallel-transported, differentiable field strengths, and it aligns with lattice observations and the stochastic vacuum framework.

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 $μ$ of a monopole and to compute its vacuum expectation value $\langle μ\rangle$ , the disorder parameter which indicates dual superconductivity. The Imechanism of confinement is dual superconductivity of vacuum if $\langle μ\rangle \neq 0 $ in the confined phase , and $\langle μ\rangle =0$ 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.