Renormalization of supersymmetric gauge theories on orbifolds: Brane gauge couplings and higher derivative operators

We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S1/Z2. This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T2/ZN orbifolds using supergraph techniques in six dimensions. On general ZN orbifolds the gauge couplings do renormalize at the fixed points, except for the Z2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.