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 six-dimensional N=1 super-Yang-Mills theory with the gauge group SO(N⃗∞). We also analyze the supersymmetry algebra and BPS states in the light-cone gauge.