Dual superconductor models of color confinement

Abstract

The lectures, delivered at ECT (European Centre for Theoretical Studies in Nuclear Physics and Related Areas) in Trento (Italy) in 2002 and 2003, are addressed to physicists who wish to acquire a minimal background to understand present day attempts to model the confinement of quantum chromo-dynamics (QCD) in terms of dual superconductors. The lectures focus more on the models than on attempts to derive them from QCD. They discuss the Dirac theory of magnetic monopoles, the world sheet swept out by Dirac strings, deformations of Dirac strings and charge quantization, gauge fields associated to the field tensor and to the dual field tensor, the Landau-Ginzburg (Abelian Higgs) model of a dual superconductor, the flux tube joining two equal and opposite color-electric charges, the Abrikosov-Nielsen-Olesen vortex, the divergencies of the London limit, the comparison of the calculated flux tube and string tension with lattice data, duality transformations and the use of Kalb-Ramond fields, the two-potential Zwanziger formalism, abelian gauge fixing and abelian projection, the occurence of monopoles in an abelian gauge, the maximal abelian gauge, and the confinement of static SU(3) color charges.