Probing the center-vortex area law in d=3: The role of inert vortices
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States)
In center-vortex theory, beyond the simplest picture of confinement several conceptual problems arise that are the subject of this paper. Recall that confinement arises through configuration averaging of phase factors associated with the gauge center group, raised to powers depending on the total Gauss link number of a vortex ensemble with a given Wilson loop. The simplest approach to confinement counts this link number by counting the number of vortices, considered in d=3 as infinitely long closed self-avoiding random walks of fixed step length, piercing any surface spanning the Wilson loop. Problems arise because a given vortex may pierce a given spanning surface several times without being linked or without contributing a nontrivial phase factor, or it may contribute a nontrivial phase factor appropriate to a smaller number of pierce points. We estimate the dilution factor {alpha}, due to these inert or partially inert vortices, that reduces the ratio of fundamental string tension K{sub F} to the areal density {rho} of vortices from the ratio given by elementary approaches and find {alpha}=0.6{+-}0.1. Then we show how inert vortices resolve the problem that the link number of a given vortex-Wilson-loop configuration is the same for any spanning surface of whatever area, yet a unique area (of a minimal surface) appears in the area law. Third, we discuss semiquantitatively a configuration of two distinct Wilson loops separated by a variable distance, and show how inert vortices govern the transition between two possible forms of the area law (one at small loop separation, the other at large), and point out the different behaviors in SU(2) and higher groups, notably SU(3). The result is a finite-range van der Waals force between the two loops. Finally, in a problem related to the double-loop problem, we argue that the analogs of inert vortices do not affect the fact that, in the SU(3) baryonic area law, the mesonic string tension appears.
- OSTI ID:
- 20782675
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 73, Issue 6; Other Information: DOI: 10.1103/PhysRevD.73.065004; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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