Boundary conditions in the Mirabelli and Peskin model

TL;DR

This paper reformulates the Mirabelli and Peskin supersymmetric model using boundary superfields, avoiding delta(0) ambiguities and naturally deriving boundary conditions consistent with supersymmetry.

Contribution

It presents a boundary (interval) formulation of the Mirabelli-Peskin model that is free of delta(0) ambiguities and derives boundary conditions from the variational principle.

Findings

Boundary conditions follow from the variational principle and are supersymmetry closed.

The formulation naturally incorporates Gibbons-Hawking-like boundary terms.

The model remains supersymmetric without imposing boundary conditions off-shell.

Abstract

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!).