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arXiv · 1909.04074

Testing Macdonald Index as a Refined Character of Chiral Algebra

Akimi Watanabe·Rui-Dong Zhu
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Abstract

We test in $(A_{n-1},A_{m-1})$ Argyres-Douglas theories with $\mathrm{gcd}(n,m)=1$ the proposal of Song's in arXiv:1612.08956 that the Macdonald index gives a refined character of the dual chiral algebra. In particular, we extend the analysis to higher rank theories and Macdonald indices with surface operator, via the TQFT picture and Gaiotto-Rastelli-Razamat's Higgsing method. We establish the prescription for refined characters in higher rank minimal models from the dual $(A_{n-1},A_{m-1})$ theories in the large $m$ limit, and then provide evidence for Song's proposal to hold (at least) in some simple modules (including the vacuum module) at finite $m$. We also discuss some observed mismatch in our approach.

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Akimi Watanabe, Rui-Dong Zhu. 2019-09-09. Testing Macdonald Index as a Refined Character of Chiral Algebra. https://doi.org/10.1007/jhep02(2020)004

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