Matrix Regularization of Open Supermembrane — towards M - theory five - brane via open supermembrane —

We study open supermembrane in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving, in the GreenSchwarz formalism, the boundary conditions of open superstring in the type IIA theory, we determine the boundary conditions of open supermembrane by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply self-duality of the three-form field strength on the five-brane world volume. We show that the light-cone gauge formulation is regulated by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N→ ∞). We also analyze SUSY algebra and BPS states in the light-cone gauge. hep-th/9707200 JSPS fellow † e-mail address : [email protected] ‡ e-mail address : [email protected] § e-mail address : [email protected]