New results on superconformal quivers

TL;DR

This paper classifies superconformal quivers, introduces a 'shrinking' procedure to generate new models, and proves the completeness of the list of 3 and 4 block quivers, linking them to D3 branes on CY singularities.

Contribution

It systematically studies superconformal quivers, introduces the 'shrinking' method to find new models, and proves the classification is complete for 3 and 4 block cases.

Findings

Number of superconformal 3 block quivers is 16, not 14.

Introduced 'shrinking' procedure to generate new quivers.

All rank 2 chiral quivers are either del Pezzo or derived from del Pezzo quivers.

Abstract

All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting 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 the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk'' del Pezzo models exist.