On low rank 4d $\mathcal{N}=2$ SCFTs

TL;DR

This paper systematically classifies low rank 4d $ abla=2$ superconformal field theories using class-S and string theory constructions, deriving formulas and physical properties, and predicting new algebraic isomorphisms.

Contribution

It provides a universal formula for the rank of these theories and computes their physical quantities, expanding the understanding of low rank 4d $ abla=2$ SCFTs.

Findings

Universal formula for the rank of low rank 4d $ abla=2$ SCFTs

Computed central charges, flavor symmetries, and vertex operator algebras

Predicted new isomorphisms of 2d vertex operator algebras

Abstract

There are two major ways of constructing 4d $\mathcal{N}=2$ 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.