A New Orientifold of $C^{2}/Z_{N}$ and Six-dimensional RG Fixed Points

We discuss the consistency conditions of a novel orientifold projection of type IIB string theory on C^2/Z_N singularities, in which one mods out by the combined action of world-sheet parity and a geometric operation which exchanges the two complex planes. The field theory on the world-volume of D5-brane probes defines a family of six-dimensional RG fixed points, which had been previously constructed using type IIA configurations of NS-branes and D6-branes in the presence of O6-planes. Both constructions are related by a T-duality transforming the set of NS-branes into the C^2/Z_N singularity. We also construct additional models, where both the standard and the novel orientifold projections are imposed. They have an interesting relation with orientifolds of D_K singularities, and provide the T-duals of certain type IIA configurations containing both O6- and O8-planes.