On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
Combinatorics
2026-05-27 v2 High Energy Physics - Theory
Number Theory
Abstract
We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type , 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.
Keywords
Cite
@article{arxiv.2605.02251,
title = {On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories},
author = {Shane Chern and Chanh Tran and Tanay Wakhare},
journal= {arXiv preprint arXiv:2605.02251},
year = {2026}
}