Boundary conditions in supergravity on a manifold with boundary
  We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary (``downstairs'') and orbifold (``upstairs'') pictures, we present a bulk-plus-boundary/brane action for the five-dimensional (on-shell) supergravity which is supersymmetric with the use of fewer boundary conditions than were previously employed. The required Gibbons-Hawking-like Y-term and many other aspects of the boundary/orbifold picture correspondence are discussed. 
Dmitry V. Belyaev