Chiral fermions, orbifolds, scalars, and fat branes

We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five-dimensional model, which has chiral fermion zero modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the Kaluza-Klein expansion in some detail. We find that there are, in general, non-zero-mode states stuck to the brane, just as the chiral zero mode is. We see explicitly the transition from the states dominated by the internal structure of the fat brane to those dominated by the compactification.