M ( atrix ) Theory on an Orbifold and Twisted Membrane 1

M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on S1/Z2 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. 1 Work supported in part by the Department of Energy Contract DE-AC03-76SF00515, NSF Grant PHY9219345, U.S.NSF-KOSEF Bilateral Grant, KOSEF Purpose-Oriented Research Grant 94-1400-04-01-3 and SRC-Program, and the Seoam Foundation Fellowship.