Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories

Abstract

We brute-force evaluate the vacuum character for $\mathcal{N}=2$ vertex operator algebras labelled by crystallographic complex reflection groups $G(k,1,1)={\mathbb{Z}}_k$, $k=3,4,6$, and $G(3,1,2)$. For ${\mathbb{Z}}_{3,4}$ and $G(3,1,2)$ these vacuum characters have been conjectured to respectively reproduce the Macdonald limit of the superconformal index for rank one and rank two S-fold $\mathcal{N}=3$ theories in four dimensions. For the ${\mathbb{Z}}_3$ case, and in the limit where the Macdonald index reduces to the Schur index, we find agreement with predictions from the literature.

arXiv comment5 pages, 1 figure, 3 supplementary Mathematica notebooks; v2: minor corrections, v3: notebook links to ope.math and OPEdefs packages fixed and new results summary notebook included

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Cited by in corpus (5)

• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Higgs, Coulomb, and Hall-Littlewood
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories