Argyres-Douglas theories, the Macdonald index, and an RG inequality

We conjecture closed-form expressions for the macdonald limits of the super-conformal 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 two s-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the su(2) r currents and flavor symmetry moment maps, and we find a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. in addition, we show that the hall-littlewood limits of our indices are equivalent to the corresponding higgs branch hilbert series. we explain this fact by considering the s 1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. finally, we comment on the implications of our work for more general $$ mathcal{n}=2 $$ superconformal field theories.