The Baryon Wilson Loop Area Law in QCD

John M. Cornwall

doi:10.1103/PhysRevD.54.6527

paper

The Baryon Wilson Loop Area Law in QCD

arXiv:hep-th/9605116 · doi:10.1103/PhysRevD.54.6527

Abstract

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 $exp [- K A_{Y}]$ , where $K$ is the $q q ˉ$ 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 ( $Δ$ 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 $Δ$ law from the usual vortex-monopole picture of confine- ment, and show that in any case because of the 1/2 in the $Δ$ 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 $Δ$ law. Finally, we extend these considerations, including perturbative contributions, to gauge groups $S U (N)$ , with $N > 3$ .

26 pages, Latex plus three .eps figures in a uuencoded file. Only change from original submission is addition of reference to work of M. B. Halpern (Phys. Lett. 81B, 245 (1979); Phys. Rev. D19, 517 (1979)

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String Tension and Chern-Simons Fluctuations in the Vortex Vacuum of d=3 Gauge Theory

The Baryon Wilson Loop Area Law in QCD

Abstract

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