Boundary terms for supergravity and heterotic M-Theory

This paper considers eleven dimensional supergravity on a manifold with boundary and the theories related to heterotic $M$-theory, in which the matter is confined to the boundary. New low energy actions and boundary conditions on supergravity fields are derived. Previous problems with infinite constants in the action are overcome. The new boundary conditions are shown to be consistent with supersymmetry, and their role in the ten dimensional reduction and gaugino condensation is briefly discussed.