5 The Confinement of SU(3) Color Charges

Abstract

If we wish to describe color confinement in terms of the Meissner effect of a dual superconductor, we need to adapt the Landau-Ginzburg model to the dynamics of quarks and gluons, so as to accommodate their color quantum numbers. The action (3.1) of the Landau-Ginzburg model describes a U(1) gauged self-interacting complex scalar field ψ . Since the magnetic current of the dual superconductor is somehow related to the monopoles which are formed by topological defects in a given gauge, as described in Sect. 4.1, it might make sense to restrict the covariant derivative D _μ to the corresponding abelian gauge. An adaptation of the Landau-Ginzburg model to color SU(3) , which respects Weyl symmetry, was proposed in the 1989 paper of Maedan and Suzuki [10]. It was further developed in the 1993 paper of Kamizawa, Matsubara, Shiba and Suzuki [108] and the 1999 papers of Chernodub and Komarov [109, 110]. We shall first present the model in the absence of quark charges. The latter will be introduced in Sect. 5.2.