Yang-Mills Integrals

TL;DR

This paper explores SU(N) Yang-Mills integrals, using Monte Carlo methods to analyze their properties, including partition functions and eigenvalue distributions, with new exact results for SU(2) and preliminary Wilson loop computations.

Contribution

It introduces Monte Carlo techniques to study Yang-Mills integrals and derives new exact results for SU(2) eigenvalue distributions.

Findings

Derived new exact results for SU(2) eigenvalue distributions

Used Monte Carlo methods to analyze partition functions

Reported preliminary Wilson loop computations

Abstract

SU(N) Yang-Mills integrals form a new class of matrix models which, in their maximally supersymmetric version, are relevant to recent non-perturbative definitions of 10-dimensional IIB superstring theory and 11-dimensional M-theory. We demonstrate how Monte Carlo methods may be used to establish important properties of these models. In particular we consider the partition functions as well as the matrix eigenvalue distributions. For the latter we derive a number of new exact results for SU(2). We also report preliminary computations of Wilson loops. (Based on talk presented by M. Staudacher at Strings '99, Potsdam, July 19-24 1999)