Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond

Abstract

We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\hat{\Gamma }(G)$ labeled by a pair of simply-laced Lie groups $\Gamma$ and $G$. They are constructed out of gauging a number of ${\mathcal{D}}_p(G)$ and $(G,G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $\Gamma =D_4,E_6,E_7,E_8$ and some special choices of $G$, the resulting theories have identical central charges $(a=c)$ without taking any large $N$ limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of $\mathcal{N}=4$ super Yang--Mills theory upon rescaling fugacities. Especially, we find that the Schur index of ${\hat{D}}_4(SU(N))$ theory for $N$ odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasi-modular. 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 an ALE singularity of type $\Gamma$. We also comment on a tantalizing connection regarding the theories labeled by $\Gamma$ in the Deligne--Cvitanović exceptional series.

33pages+appendix, 8 tables, 4 figures

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Cited by in corpus (10)

• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• The exact Schur index in closed form
• $\mathcal{N}=2^{\ast }$ Schur indices
• Holographic duals of M5-branes on an irregularly punctured sphere
• Higgs, Coulomb, and Hall-Littlewood
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• Infinitely many 4d N=1 SCFTs with a=c
• Emergent N=4 supersymmetry from N=1
• Generalized symmetry constraints on deformed 4d (S)CFTs
• A landscape of 4d N=1 SCFTs with a=c