ar X iv : h ep - t h / 96 05 11 6 v 2 1 7 M ay 1 99 6 The Baryon Wilson Loop Area Law in QCD
نویسنده
چکیده
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[−KAY ], where K is the qq̄ string tension and AY 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)(A12 +A13 +A23)], where, e.g., A12 is the minimal area between quark lines 1 and 2 (∆ 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 ∆ law from the usual vortex-monopole picture of confinement, and show that in any case because of the 1/2 in the ∆ 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 ∆ law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU(N), with N > 3. UCLA/96/TEP/15 May 1996 * Electronic address: [email protected]
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ar X iv : h ep - t h / 96 05 11 6 v 1 1 6 M ay 1 99 6 The 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[−KAY ], where K is the qq̄ string tension and AY is the global minimum area, generically a three-bladed area with the blades joined along a Steiner line (Y configuration). However, the...
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