A Matrix Model for Heterotic $Spin(32)/Z_2$ and Type I String Theory

TL;DR

This paper constructs matrix models for heterotic Spin(32)/Z_2 and E8 string theories, as well as type I string theory, revealing their gauge structures, Wilson line effects, and the emergence of an 11th dimension at strong coupling.

Contribution

It derives explicit matrix models for heterotic and type I string theories, including Wilson line effects and the emergence of an extra dimension in the E8 case.

Findings

Matrix model for Spin(32)/Z_2 heterotic string as O(N) gauge theory on D-strings.

Wilson line effects shift the momentum sector in the matrix model.

E8 heterotic string develops an 11th dimension at strong coupling.

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 $\e8$ 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 $\e8$ theory, and not the Spin(32)/$Z_2$, develops an 11'th 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.