  We study higher dimensional field theories with extra dimensions from a 4d
spectrum point of view. It is shown that 4d mass spectra of spinor, gauge and
gravity field theories are governed by quantum-mechanical supersymmetry. The 4d
massless modes turn out to correspond to zero energy vacuum states of the
supersymmetry. Allowed boundary conditions on extra dimensions compatible with
the supersymmetry are found to be severely restricted.
