Quantization and High Energy Unitarity in Orbifold Theories

Abstract

We study five-dimensional Yang-Mills theories compactified on an S^1/Z_2 orbifold. The fundamental Lagrangian naturally includes brane kinetic terms at the orbifold fixed points which are induced by quantum corrections of the bulk fields. The theories are quantized in the higher-dimensional R_xi gauges before compactification. Using Ward and Slavnov-Taylor identities, an all-order proof of a generalized equivalence theorem is presented. The theorem relates scattering amplitudes of longitudinal Kaluza-Klein gauge bosons to amplitudes of the corresponding scalar modes. Non-trivial sum rules among the fundamental couplings of the 4D effective theory lie at the heart of high energy unitarity cancellations. Using a novel coupled channel analysis, we derive an upper bound on the number of Kaluza-Klein modes from perturbative unitarity. The bound shows a very weak dependence on the size of the brane kinetic terms.