Abstract
We conjecture closed-form expressions for the Macdonald limits of the superconformal 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 N=2 superconformal field theories.
Highlights
When they were first constructed, Argyres-Douglas (AD) theories were defined as singular points on the Coulomb branches of certain N = 2 gauge theories where mutually non-local BPS states become massless [1, 2]
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
We considered the topological quantum field theory living on C (in this case, two-dimensional q-deformed SU(2) Yang-Mills theory (YM) [10]) and defined a state in this theory corresponding to the irregular singularity
Summary
In generic N = 2 theories, this result suggests a new criterion for the absence of index contributions due to exotic D type HL operators (in the notation of [14]) and, possibly, a new constraint on RG flows between four and three dimensions that preserve eight supercharges Another important aspect of our previous work [5] involved a comparison of the Schur indices of the (A1, A3) and (A1, D4) theories with the torus partition function of the corresponding two-dimensional chiral algebras (in the sense of [18]).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have