Partition Functions of Reduced Matrix Models with Classical Gauge Groups

Abstract

We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d=4 N=1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1) and USp(2N). The integrals reduce to those over the maximal tori by semi-classical approximation which is exact in reduced models. We carry out residue calculus by developing a diagrammatic method, in which the action of the Weyl groups and therefore counting of multiplicities are explained obviously.