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2019

Testing Macdonald Index as a Refined Character of Chiral Algebra

Watanabe, Akimi, Zhu, Rui-Dong

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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.

Testing Macdonald Index as a Refined Character of Chiral Algebra · Around

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