Orientifolding the conifold

In this paper we study the N=1 supersymmetric field theories realized on the world-volume of type IIB D3-branes sitting at orientifolds of non-orbifold singularities (conifold and generalizations). Several chiral models belong to this family of theories. These field theories have a T-dual realization in terms of type IIA configurations of relatively rotated NS fivebranes, D4-branes and orientifold six-planes, with a compact x6 direction, along which the D4-branes have finite extent. We compute the spectrum of the D3-branes directly in the type IIB picture and match the resulting field theories with those obtained in the type IIA setup, thus providing a non-trivial check of this T-duality. Since the usual techniques to compute the spectrum of the model and check the cancellation of tadpoles cannot be applied to the case of orientifolds of non-orbifold singularities, we use a different approach, and construct the models by partially blowing up orientifolds of C3/Z2xZ2 and C3/Z2xZ3) orbifolds