Yang-Mills integrals

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.