On an interval compactification in supersymmetric theory, boundary conditions
for bulk fields must be treated carefully. If they are taken arbitrarily
following the requirement that a theory is supersymmetric, the conditions could
give redundant constraints on the theory. We construct a supersymmetric action
integral on an interval by introducing brane interactions with which total
derivative terms under the supersymmetry transformation become zero due to a
cancellation. The variational principle leads equations of motion and also
boundary conditions for bulk fields, which determine boundary values of bulk
fields. By estimating mass spectrum, {\it spontaneous} supersymmetry breaking
in this simple setup can be realized in a new framework. This supersymmetry
breaking does not induce massless R-axion, which is favorable for
phenomenology. It is worth noting that fermions in hyper-multiplet, gauge
bosons, and the fifth-dimensional component of gauge bosons can have zero-modes
(while the other components are all massive as Kaluza-Klein modes), which fits
the gauge-Higgs unification scenarios.Comment: 9 pages, a clarification about boundary conditions adde