Five-Brane Superpotentials in Heterotic M-Theory

The open supermembrane contribution to the non-perturbative superpotential of bulk space five-branes in heterotic M-theory is presented. We explicitly compute the superpotential for the modulus associated with the separation of a bulk five-brane from an end-of-the-world three-brane. The gauge and kappa-invariant boundary strings of such open supermembranes are given and the role of the holomorphic vector bundle on the orbifold fixed plane boundary is discussed in detail.