On Gauge Bosons in the Matrix Model Approach to M Theory

We discuss the appearance of $E_8\times E_8$ gauge bosons in Banks, Fischler, Shenker, and Susskind's zero brane quantum mechanics approach to M theory, compactified on the interval $S^1/Z_2$. The necessary bound states of zero branes are proven to exist by a straightforward application of T-duality and heterotic $Spin(32)/Z_2$-Type I duality. We then study directly the zero brane Hamiltonian in Type I' theory. This Hamiltonian includes couplings between the zero branes and background Dirichlet 8 branes localized at the orientifold planes. We identify states, localized at the orientifold planes, with the requisite gauge boson quantum numbers. An interesting feature is that $E_8$ gauge symmetry relates bound states of different numbers of zero branes.