From baglike models to the large-Nc limit via the Abelian projection.

Abstract

't Hooft proposed a model where quarks are confined by a chromomagnetic Meissner effect along the N-1 U(1) directions of the maximal Abelian subgroup of SU(N). This is the Abelian projection. I show that this model successfully interpolates from low N, where quarks are confined in a baglike region of perturbative vacuum embedded in the true nonperturbative vacuum, to the large-N limit. At large N quarks are confined in a ''shallow'' nonperturbative medium and the string tension is an N-independent constant. Confinement of adjoint quarks also properly evolves from screening at small N to confinement at infinite N with a string tension twice as large as for quarks in the fundamental representation.