2004/11/29 by Sergio Benvenuti, Amihay Hanany
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Block (permutation group theory) #Brane cosmology #Field (mathematics) #Fixed point #Homotopy and Cohomology in Algebraic Topology #Quiver #Rank (graph theory) #Statement (logic) #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/04/032
published as JHEP0604:032,2006 · 51 pages, many figures
arxiv created 2004/11/29 · openalex publication_date 2006/04/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.