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We conjecture closed-form expressions for the Macdonald limits of thesuperconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas(AD) theories in terms of certain simple deformations of Macdonald polynomials.As checks of our conjectures, we demonstrate compatibility with twoS-dualities, we show symmetry enhancement for special values of n, and we arguethat our expressions encode a non-trivial set of renormalization group flows.Moreover, we demonstrate that, for certain values of n, our conjectures implysimple operator relations involving composites built out of the SU(2)_Rcurrents and flavor symmetry moment maps, and we find a consistent picture inwhich these relations give rise to certain null states in the correspondingchiral algebras. In addition, we show that the Hall-Littlewood limits of ourindices are equivalent to the corresponding Higgs branch Hilbert series. Weexplain this fact by considering the S^1 reductions of our theories and showingthat the equivalence follows from an inequality on monopole quantum numberswhose coefficients are fixed by data of the four-dimensional parent theories.Finally, we comment on the implications of our work for more general N=2superconformal field theories.

Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality