Matrix model superpotentials and ADE singularities

We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain much of Intriligator and Wecht's ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. We find that ADE superpotentials in the Intriligator-Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau with corresponding ADE singularities. Moreover, in the additional Ô, Â, D̂ and Ê cases we find new singular geometries. These "hat" geometries are closely related to their ADE counterparts, but feature non-isolated singularities. As a byproduct, we give simple descriptions for small resolutions of Gorenstein threefold singularities in terms of transition functions between just two co-ordinate charts. To obtain these results we develop an algorithm for blowing down exceptional P¹, described in the appendix.