Extra-dimensional theories contain a number of almost degenerate states at each Kaluza-Klein level. If extra dimensional momentum is at least approximately conserved then the phenomenology of such nearly degenerate states depends crucially on the mass splittings between KK modes. We calculate the complete one-loop radiative corrections to KK masses in general 5 and 6 dimensional theories. We apply our formulas to the example of universal extra dimensions and show that the radiative corrections are essential to any meaningful study of the phenomenology. Our calculations demonstrate that Feynman diagrams with loops wrapping the extra dimensions are well-defined and cutoff independent even though higher dimensional theories are not renormalizable.

It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory. We show that this expectation is violated in theories where the Standard Model elds are conned to a thick w all in extra dimensions, with the fermions \stuck" at dierent points in the wall. Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions. This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography. A model independent prediction of this scenario is non-universal couplings of the Standard Model fermions to the \Kaluza-Klein" excitations of the gauge elds. This allows a measurement of the fermion locations in the extra dimensions at the LHC or NLC if the wall thickness is close to the TeV scale.

We propose a new framework for mediating supersymmetry breaking through an extra dimension. It predicts positive scalar masses and solves the supersymmetric flavor problem. Supersymmetry breaks on a "source" brane that is spatially separated from a parallel brane on which the standard model matter fields and their superpartners live. The gauge and gaugino fields propagate in the bulk, the latter receiving a supersymmetry breaking mass from direct couplings to the source brane. Scalar masses are suppressed at the high scale but are generated via the renormalization group. We briefly discuss the spectrum and collider signals for a range of compactification scales. *