New perspectives on Yang-Mills theories with sixteen supersymmetries

We describe various approaches that give matrix descriptions of compactifiedNS five-branes. As a result, we obtain matrix models for Yang-Mills theorieswith sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence ofthe various approaches relates the Coulomb branch of certain gauge theories tothe moduli space of instantons on $T^4$. We also obtain an equivalence betweencertain six-dimensional string theories. Further, we discuss how variousperturbative and non-perturbative features of these Yang-Mills theories appearin their matrix formulations. The matrix model for four-dimensional Yang-Millsis manifestly S-dual. In this case, we describe how electric fluxes, magneticfluxes and the interaction between vector particles are realized in the matrixmodel.Comment: 44 pages, harvmac; references adde