Theory of Color Confinement: State of the Art

An almost general consensus exists on the idea that deconfinement is an order disorder transition. The present experimental upper limits on the observation of free quarks are 15 orders of magnitude smaller than what is expected in the absence of confinement. The only natural interpretation is that confinement is an absolute property relying on symmetry. The confined phase of QCD is disordered (strong coupling). The symmetry of a disordered phase can be understood in terms of duality. The system should admit non local topological excitations, and, besides the usual description in terms of local fields a complementary dual description exists in which the topological excitations become local and their v.e.v. are the order parameters. The dual effective coupling constant gD is related to g as gD ∼ 1/g. The strong coupling regime is mapped into the weak coupling of the dual description. If this is correct, the ultimate goal is to identify the dual excitations which condense in the confined phase, or at least to identify their quantum numbers, i.e. the symmetry of the confining vacuum. On the basis of the above argument we shall disregard all the approaches to the problem which are not based on symmetry. Two possibilities are being considered for the dual symmetry, which in principle are not mutually exclusive