Partition Functions of Reduced Matrix Models with Classical Gauge Groups

TL;DR

This paper computes the exact partition functions of reduced matrix models derived from 4D N=1 super Yang-Mills theories with classical gauge groups, using residue calculus and diagrammatic methods.

Contribution

It introduces a diagrammatic residue calculus approach to evaluate partition functions of matrix models with classical gauge groups, clarifying Weyl group actions.

Findings

Exact partition functions for SO(2N), SO(2N+1), USp(2N) models obtained.

A diagrammatic method simplifies residue calculations and accounts for Weyl group symmetries.

Provides a systematic way to evaluate matrix model integrals in supersymmetric gauge theories.

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.