CASIMIR SCALING VERSUS ABELIAN DOMINANCE IN QCD STRING FORMATION

We show that the hypothesis of Abelian dominance in the maximal Abelia n gauge, which is known to work for Wilson loops in the fundamental re presentation, fails for Wilson loops in higher group representations. Monte Carlo simulations are performed on lattice SU(2) gauge theory, i n D=3 dimensions, in the maximal Abelian gauge, in the confined phase. It is well known that Creutz ratios extracted from loops in various g roup representations are proportional to the quadratic Casimir invaria nt of each representation, in a distance interval from the confinement scale to the point where color screening sets in. In contrast, we fin d numerically, in the same interval, that string tensions extracted fr om loops built from Abelian projected configurations are the same for the fundamental and j=3/2 representations, and vanish for the adjoint representation. In addition, we perform a lattice Monte Carlo simulati on of the Georgi-Glashow model in D=3 dimensions. We find that the rep resentation dependence of string tensions is that of pure Yang-Mills t heory in the symmetric phase, but changes abruptly to equal tensions f or the j=1/2, 3/2 representations, and zero tension for j=1, at the tr ansition to the Higgs phase. Our results indicate that an effective Ab elian theory at the confinement scale, invoking only degrees of freedo m (monopoles and photons) associated with a particular Cartan subalgeb ra, is inadequate to describe the actual interquark potential in an un broken non-Abelian gauge theory.