A matrix model for heterotic [formula omitted] and type I string theory

Abstract

We consider heterotic string theories in the DLCQ. We derive that the matrix model of the Spin(32)/ Z 2 heterotic theory is the theory living on N D-strings in type I wound on a circle with no Spin(32)/ Z 2 Wilson line on the circle. This is an O( N) gauge theory. We rederive the matrix model for the E 8 × E 8 heterotic string theory, explicitly taking care of the Wilson line around the lightlike circle. The result is the same theory as for Spin(32)/ Z 2 except that now there is a Wilson line on the circle. We also see that the integer N labeling the sector of the O( N) matrix model is not just the momentum around the lightlike circle, but a shifted momentum depending on the Wilson line. We discuss the aspect of level matching, GSO projections and why, from the point of view of matrix theory the E 8 × E 8 theory, and not the Spin(32)/ Z 2 , develops an 11th dimension for strong coupling. Furthermore a matrix theory for type I is derived. This is again the O( N) theory living on the D-strings of type I. For small type I coupling the system is 0+1-dimensional quantum mechanics.