Matrix theory and heterotic strings on tori

Abstract

We consider compactifications of the matrix model of M-theory on S 1/ Z 2 × T d for d > 0 , and interpret them as orbifolds of the supersymmetric U( N) Yang-Mills theory on R × 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 spacetime 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.