Generalized conifolds and four dimensional N = 1 superconformal theories

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The N = 1 superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE N = 2 superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single D3-brane and discuss the near-horizon super-gravity solution for a large number N of coincident D3-branes.