Baryon Wilson loop area law in QCD

There is still confusion about the correct form of the area law for the baryonic Wilson loop (BWL) of QCD. Strong-coupling (i.e., finite lattice spacing in lattice gauge theory) approximations suggest the form exp[-KA(Y)], where K is the q (q) over bar string tension and A(Y) is the global minimum area, generically a three-bladed area with the blades joined along a Steiner line (Y configuration). However, the correct answer is exp[-(K/2)(A(12)+A(13)+A(23))], where, e.g., A(12) is the minimal area between quark lines 1 and 2 (Delta configuration). This second answer was given long ago, based on certain approximations, and is also strongly favored in lattice computations. In the present work, we derive the Delta law from the usual vortex-monopole picture of confinement, and show that, in any case, because of the 1/2 in the Delta law, this law leads to a larger value for the BWL (smaller exponent) than does the Y law. We show that the three-bladed, strong-coupling surfaces, which are infinitesimally thick in the limit of zero lattice spacing, survive as surfaces to be used in the non-Abelian Stokes' theorem for the BWL, which we derive, and lead via this Stokes' theorem to the correct Delta law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU(N), with N>3.