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Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra
George Andrews, Anindya Banerjee, Chinmaya Bhargava, Ranveer Kumar Singh, Runkai Tao
https://arxiv.org/abs/2507.06294

Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra
In this paper, we relate the MacDonald index of a 4d $\mathcal{N}=2$ SCFT with the Hilbert series of the arc space of the Zhu algebra of the corresponding Schur VOA. Using this, we conjecture a simple formula for the MacDonald index of $(A_1,D_{2n+1})$ Argyres-Douglas theory. We perform checks of the formula against the known Schur limits and RG flows. To match the Schur limit, we prove new $q$-series identities.