Evaluation of Self-Intersecting Wilson Loop in the Stochastic Vacuum Model

Abstract

A Wilson loop is evaluated within the stochastic vacuum model for the case when the respective contour is self-intersecting and its size does not exceed the correlation length of the vacuum. The result has the form of a certain functional of the tensor area. It is similar to that for the non-self-intersecting loop only when the contour is a plane one. Even for such a contour, the obtained expression depends on the ratio of two functions parametrizing the bilocal field strength correlator taken at the origin, which is not so for the case of non-self-intersecting contour.