Matrix Regularization of an Open Supermembrane ---towards M-theory five-branes via open supermembranes ---

We study open supermembranes in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving in the Green-Schwarz formalism the boundary conditions for open superstrings in the type IIA theory, we determine the boundary conditions for open supermembranes by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply the self-duality of the three-form field strength on the five-brane world volume. We show that the light-cone gauge formulation is regularized by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N\to\infty). We also analyze the SUSY algebra and BPS states in the light-cone gauge.