Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity

Just as parallel threebranes on a smooth manifold are related to string theory on $AdS_5\times {\bf S}^5$, parallel threebranes near a conical singularity are related to string theory on $AdS_5\times X_5$, for a suitable $X_5$. For the example of the conifold singularity, for which $X_5=(SU(2)\times SU(2))/U(1)$, we argue that string theory on $AdS_5\times X_5$ can be described by a certain ${\cal N}=1$ supersymmetric gauge theory which we describe in detail.