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arXiv · 2605.02251

On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories

Shane Chern·Chanh Tran·Tanay Wakhare
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Abstract

We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type $(A_1, D_{2k+1})$, thereby yielding a conjectural fermionic formula due to Andrews et al. Our duality is built upon a new conjugate Bailey pair to be established using techniques from orthogonal polynomials and basic hypergeometric series. In addition, this fermionic formula implies another sum-like expression independently conjectured by Andrews et al. and Kim et al. for the same Macdonald index.

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Shane Chern, Chanh Tran, Tanay Wakhare. 2026-05-26. On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories. https://arxiv.org/abs/2605.02251

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