Matrix Theory and Heterotic Strings on Tori

We consider compactifications of the matrix model of M-theory on $S^1/Z_2\times T^d$ for $d>0$, and interpret them as orbifolds of the supersymmetric U(N) Yang-Mills theory on $R\times T^{d+1}$. The orbifold group acts both on the gauge group and on the $T^{d+1}$, reduces the gauge group to O(N) over 1+1 dimensional fixed-point submanifolds, and breaks half of the supersymmetry. We clarify some puzzling aspects of the gauge anomaly cancellation in the presence of space-time Wilson lines; in general, the Yang-Mills theory requires certain Chern-Simons couplings to supergravity background fields. We discuss the possibility that D8-branes are present as certain matrix configurations in the Yang-Mills theory, and the fundamental fermions emerge as zero modes. Finally, we point out that the correspondence between matrix theory and string theory suggests the existence of a multitude of non-trivial RG fixed points and dualities in orbifold Yang-Mills theories with eight supercharges in various dimensions.