Nonperturbative superpotentials from membrane instantons in heterotic M-theory

A formalism for calculating the open supermembrane contribution to the nonperturbative superpotential of moduli in heterotic M-theory is presented. This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation modulus of the end-of-the-world BPS three-branes, whose nonperturbative superpotential is computed. The role of gauge bundles on the boundaries of the open supermembranes is discussed in detail, and a topological criterion presented for the associated superpotential to be nonvanishing