Gauge threshold corrections for local orientifolds

We study gauge threshold corrections for systems of fractional branes at local orientifold singularities and compare with the general Kaplunovsky-Louis expression for locally supersymmetric = 1 gauge theories. We focus on branes at orientifolds of the c ³/z ₄, c ³/z ₆ and c ³/z ₆ ^′ singularities. We provide a CFT construction of these theories and compute the threshold corrections. Gauge coupling running undergoes two phases: one phase running from the bulk winding scale to the string scale, and a second phase running from the string scale to the infrared. The first phase is associated to the contribution of = 2 sectors to the IR β functions and the second phase to the contribution of both = 1 and = 2 sectors. In contrast, naive application of the Kaplunovsky-Louis formula gives single running from the bulk winding mode scale. The discrepancy is resolved through 1-loop non-universality of the holomorphic gauge couplings at the singularity, induced by a 1-loop redefinition of the twisted blow-up moduli which couple differently to different gauge nodes. We also study the physics of anomalous and non-anomalous U(1)s and give a CFT description of how masses for non-anomalous U(1)s depend on the global properties of cycles.