RG fixed points and flows in SQCD with adjoints

We map out and explore the zoo of possible 4d N = I superconformal theories which are obtained as RG fixed points of N = I SQCD with N-f fundamental and N-a adjoint matter representations. Using a-maximization, we obtain exact operator dimensions at all RG fixed points and classify all relevant, Landau-Ginzburg type, adjoint superpotential deformations. Such deformations can be used to RG flow to new SCFTs, which are then similarly analyzed. Remarkably, the resulting 4d SCFT classification coincides with Arnold's ADE singularity classification. The exact superconformal R-charge and the central charge a are computed for all of these theories. RG flows between the different fixed points are analyzed, and all flows are verified to be compatible with the conjectured a-theorem. (C) 2003 Elsevier B.V. All rights reserved.