Superconformal field theory on threebranes at a Calabi-Yau singularity

Just as parallel threebranes on a smooth manifold are related to string theory on AdS 5 × S 5 , parallel threebranes near a conical singularity are related to string theory on AdS5 × X 5, for a suitable X 5. For the example of the conifold singularity, for which X 5 = (SU(2) × SU(2))/U(1), we argue that string theory on AdS5 × X 5 can be described by a certain N = 1 supersymmetric gauge theory which we describe in detail.