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!).