On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913163816992768 |
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| author | Chern, Shane Tran, Chanh Wakhare, Tanay |
| author_facet | Chern, Shane Tran, Chanh Wakhare, Tanay |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_02251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories Chern, Shane Tran, Chanh Wakhare, Tanay Combinatorics High Energy Physics - Theory Number Theory 81T40, 11P84, 33D15, 33D50 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. |
| title | On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories |
| topic | Combinatorics High Energy Physics - Theory Number Theory 81T40, 11P84, 33D15, 33D50 |
| url | https://arxiv.org/abs/2605.02251 |