Infinitely many 4D N=2 SCFTs with a=c and beyond

Abstract

We study a set of four-dimensional N 1/4 2 superconformal field theories (SCFTs) Gamma<SIC>oG thorn labeled by a pair of simply laced Lie groups Gamma and G. They are constructed out of gauging a number of DpoG thorn and oG; G thorn conformal matter SCFTs; therefore, they do not have Lagrangian descriptions in general. For Gamma 1/4 D4; E6; E7; E8, and some special choices of G, the resulting theories have identical central charges (a 1/4 c) without taking any large N limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of N 1/4 4 super-Yang-Mills theory uponrescaling fugacities. Especially, we find that the Schur index of written in terms of MacMahon's generalized sum-of-divisorfunction, which is quasimodular. For generic choices of Gamma and G, it can be regarded as a generalization of the affine quiver gauge theory obtained from D3-branes probing singularity of type Gamma. We also comment on a tantalizing connection regarding the theories labeled by Gamma in the Deligne-Cvitanovic exceptional series. <SIC>D4oSUoN thorn thorn theory for N odd is