LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS

Abstract

Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including nonorientable ones. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities’ point of view, non-orientability of the manifold is equivalent to its non-compactness.