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

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 punctured Riemann surface (class-S theory), and second type IIB string 3d canonical singularity. As there interests low rank theories, we search all possibilities from above constructions. Most those engineered by class-S with irregular singularities, find universal formula for so that complete possible. We then compute various physical quantities such as central charges, flavor symmetry, associated vertex operator algebra Higgs branch, etc. One interesting consequence our results prediction many new isomorphism 2d algebra.