Boundary conditions in the Mirabelli and Peskin model

We show how the (globally supersymmetric) model of Mirabelli and Peskin can be formulated in the boundary (``downstairs'' or ``interval'') picture. The necessary Gibbons-Hawking-like terms appear naturally when using (codimension one) superfields. This formulation is free of the \delta(0) ambiguities of the orbifold (``upstairs'') picture while describing the same physics since the boundary conditions on the fundamental domain are the same. The (natural) boundary conditions follow from the variational principle and form a closed orbit under supersymmetry variation. They reduce to the ``odd =0'' boundary conditions in the absence of bulk-boundary coupling. We emphasize that the action is supersymmetric without the use of any boundary conditions in the off-shell formulation (but some boundary conditions are necessary for on-shell supersymmetry!).