Colour confinement and gauge-invariant field-strength correlations

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.