Interaction of Wilson Loops in the SU(N) Gauge Theory

Abstract

The average of two Wilson loops is expressed in terms of gauge invariant field strength correlators. Assuming the existence of finite correlation length $T_g$ and taking into account the absence of a fixed direction in colour space, we generalize the area law asymptotics for the case of the average of two Wilson loops embedded into the same plane. The results are presented in terms of averaged single Wilson loop operators in irreducible representations which correspond to the geometry of the contours. A special reduction of our results (obtained for arbitrary dimensionality of space-time) to the case of two-dimensional SU(N) theory is performed and the connection to the results existing in literature is established.