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Relativistic center-vortex dynamics of a confining area law


We offer a physicist's proof that center-vortex theory requires the area in the (quenched) Wilson-loop area law to involve an extremal area. This means that, unlike in string-theory-inspired models of confining flux tubes, area-law dynamics is determined by integrating over Wilson loops only, not over surface fluctuations for a fixed loop. Fluctuations leading to perimeter-law corrections come from loop fluctuations as well as integration over finite-thickness center-vortex collective coordinates. In d=3 (or d= 2 + 1) we exploit a contour form of the extremal area in isothermal (conformally flat metric on the surface) coordinates which is similar to d = 2 (or d = 1 + 1) QCD in many respects, except that there are both quartic and quadratic terms in the action. One major result is that at large angular momentum l in d= 3 + 1 the center-vortex extremal-area picture yields a linear Regge trajectory with a Regge slope-string tension product alpha'(0)K-F of 1/(2pi), which is the canonical Veneziano or string value. In a curious effect traceable to retardation, the quark kinetic terms in the action vanish relative to area-law terms in the large-l limit, in which light-quark masses similar toK(F)(1/2) are negligible. This corresponds to string-theoretic expectations, even though we emphasize that the extremal-area law is not a string theory quantum mechanically. We show how some quantum trajectory fluctuations as well as nonleading classical terms for finite mass yield corrections scaling with l(-1/2). We compare to old semiclassical calculations of relativistic (massless) q (q) over bar bound states at large l, which also yield asymptotically linear Regge trajectories, finding agreement with a naive string Picture (classically., not quantum mechanically) and disagreement with an effective-propagator model. We show that contour forms of the area law can be expressed in terms of Abelian gauge potentials, and we relate this to old work of Comtet.

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