vortices and confinement vs . screening

Confinement in QCD is due to a condensate of thick vortices with fluxes in the center of the gauge group (center vortices), as proposed long ago by the author and others. It is well-known that such vortices lead to an area law for fundamental-representation Wilson loops, but what happens for screened (e.g., adjoint) Wilson loops has been less clear, and confusion has arisen over the large-N limit. We study the adjoint and fundamental Wilson loops for gauge group SU(N) with general N , where there are N −1 distinct vortices, whose properties (including collective coordinates and actions) we discuss. In d = 2 we construct a center-vortex model by hand so that it has a smooth large-N limit of fundamental-representation Wilson loops and find, as expected, confinement. Extending an earlier work by the author, we construct the adjoint Wilson-loop potential in this d = 2 model for all N , as an expansion in powers of ρ/M, where ρ is the vortex density per unit area and M is the gauge-boson mass (inverse vortex size) and find, as expected, screening. (This is, in fact, unexpected in d = 2 QCD.) The leading term of the adjoint potential shows a roughly linear regime followed by string breaking when the potential energy is about 2M . This leading potential is a universal (N -independent at fixed KF ) function of the type (KF/M)U(MR), where R is the spacelike dimension of a rectangular adjoint Wilson loop and KF is the *E-mail address: [email protected] UCLA/97/TEP/30 December, 1997