M(atrix) Theory on an Orbifold and Twisted Membrane

M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on ${\bf S}_1/ {\bf Z}_2$ relevant to strongly coupled heterotic and dual Type IA string theories. By analyzing orbifold condition on Chan-Paton factors, we show that three choices of gauge group are possible for heterotic M(atrix) theory: $SO(2N)$, $SO(2N+1)$ or $USp(2N)$. By examining area-preserving diffeomorphism that underlies the M(atrix) theory, we find that each choices of gauge group restricts possible topologies of two-branes. The result suggests that only the choice of $SO(2N +1)$ group allows open two-branes, hence, relevant to heterotic M(atrix) theory. We also argue that supersymmetry and vacuum energy cancellation require introduction of 8 fundamental representation spinors and their images at each boundaries. Twisted and closed two-brane configurations are obtained in the large N limit.