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 μ of a monopole and to compute its vacuum expectation value ⟨ μ ⟩, the disorder parameter which indicates dual superconductivity. The mechanism of confinement is dual superconductivity of vacuum if ⟨ μ ⟩ ≠ 0 in the confined phase, and 〈 μ 〉 = 0 in the deconfined phase. Confinement has to be certified by independent methods. This procedure works well in compact U (1) gauge theory, as proved by numerical results on the lattice and by analytic treatments. In QCD and more generically in SU ( N ) gauge theories with N > 1 there are infinitely many monopoles, one for each SU (2) subgroup of the gauge group (Abelian Projection), and for decades it has not been clear which ones would condense to make the vacuum a dual superconductor. Attempts based on technically convenient assumptions, like equivalence of all abelian projections, led to pathologies like spurious infrared divergences spoiling the existence of the thermodynamical limit. Only recently it was realised that gauge invariance forbids most of the choices for the abelian projections and fixes it up to a global group transformation. The field strengths are replaced in this approach by gauge invariant field strengths, which are their parallel transports to infinity. The resulting disorder parameter can be expressed in terms of 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 correlation functions. 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.