Random walks of Wilson loops in the screening regime

Abstract

Dynamics of Wilson loops in pure Yang-Mills theories is analyzed in terms of random walks of the holonomies of the gauge field on the gauge group manifold. It is shown that such random walks should necessarily be free. The distribution of steps of these random walks is related to the spectrum of string tensions of the theory and to certain cumulants of Yang-Mills curvature tensor. It turns out that when colour charges are completely screened, the holonomies of the gauge field can change only by the elements of the group center, which indicates that in the screening regime confinement persists due to thin center vortices. Thick center vortices are also considered and the emergence of such stepwise changes in the limits of infinitely thin vortices and infinitely large loops is demonstrated.Comment: Major revision of the previous version, to appear in Nucl. Phys. B (10 pages RevTeX, 3 figures

Center vortices as rigid strings

“…On the other hand, closed magnetic strings, or center vortices, can be directly detected [3] and seem to be thin [4]. A model-independent argument in favor of physically thin center vortices in continuum pure Yang-Mills theory was proposed recently in [5]. It is known that the full QCD string tension is reproduced with sufficiently good precision if one considers only the contribution due to topologically nontrivial winding of center vortices and Wilson loop [3,6].…”