On low rank 4d N=2 SCFTs

There are two major ways of constructing 4d N = 2 superconformal field theories (SCFTs): the first one is putting a 6d (2, 0) theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string theory on a 3d canonical singularity. As there are interests on low rank theories, we search all the possibilities from above two constructions. Most of those theories are engineered by class-S theory with irregular singularities, and we find a universal formula for the rank of theory so that a complete search is possible. We then compute various physical quantities of those theories, such as the central charges, flavor symmetry, associated vertex operator algebra and Higgs branch, etc. One of interesting consequence of our results are the prediction of many new isomorphism of 2d vertex operator algebra.

Automated summary

There are two major ways to construct 4d N = 2 superconformal field theories: placing a 6d (2, 0) theory on a punctured Riemann surface (class-S theory), and placing type IIB string theory on a 3d canonical singularity. We search all possibilities from these two constructions to study low rank theories, mostly engineered by class-S theory with irregular singularities. We find a universal formula for the theory rank, enabling a complete search, and compute various physical quantities such as central charges, flavor symmetry, vertex operator algebra, and Higgs branch. An interesting consequence is the prediction of new isomorphisms of 2d vertex operator algebras.