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In center vortex theory, beyond the simplest picture of confinement severalconceptual problems arise that are the subject of this paper. Confinementarises through averaging of phase factors which are gauge-group center elementsraised to the power of the Gauss linking numbers of vortices. The simplestapproach to confinement counts this link number by counting the number ofvortices, considered in d=3 as infinitely-long closed self-avoiding randomwalks on a cubical lattice, piercing any surface spanning the Wilson loop. Agiven vortex, however, may pierce the spanning surface multiply with a linknumber smaller than the number of piercings. We call such vortices inert(although they may be only partially-inert). We estimate the dilution factorfrom inert vortices that reduces the ratio of fundamental string tension tovortex areal piercing density as roughly 0.6. Next we show how inert vorticesresolve the old problem that the link number of a given vortex configuration isthe same for any choice of spanning surface, yet only one such surface appearsin the Wilson loop expectation value. Third, we discuss semi- quantitatively aconfiguration of two distinct Wilson loops separated by a variable distance,and show how inert vortices govern the transition between two allowed forms ofthe area law, one at small separation and one at large. The result is afinite-range Van der Waals force between the loops. Finally, in a problemrelated to the double-loop problem, we argue that inert vortices do not affectthe fact that in the SU(3) baryonic area law, the mesonic string tensionappears.Comment: Inconsistent notation and typos repaired. No changes in conclusions.  18 pages, revtex4, 5 .eps figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Probing the center-vortex area law in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math>: The role of inert vortices

Probing the center-vortex area law ind=3: The role of inert vortices