Quantum corrections to non-Abelian SUSY theories on orbifolds

We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S1/Z2 and T2/ZN, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the ZN fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non-Z2 fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.