New results on superconformal quivers

All superconformal quivers are shown to satisfy the relation c = a and arethus good candidates for being the field theory living on D3 branes probing CYsingularities. We systematically study 3 block and 4 block chiral quivers whichadmit a superconformal fixed point of the RG equation. Most of these theoriesare known to arise as living on D3 branes at a singular CY manifold, namelycomplex cones over del Pezzo surfaces. In the process we find a procedure ofgetting a new superconformal quiver from a known one. This procedure is termed"shrinking" and, in the 3 block case, leads to the discovery of two new models.Thus, the number of superconformal 3 block quivers is 16 rather than thepreviously known 14. We prove that this list exausts all the possibilities. Wesuggest that all rank 2 chiral quivers are either del Pezzo quivers or can beobtained by shrinking a del Pezzo quiver and verify this statement for all 4block quivers, where a lot of "shrunk'' del Pezzo models exist.