On the superconformal index of Argyres–Douglas theories

We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A₁, A₂₍-₃) and the (A₁, D₂₍) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N=2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A₁, A₂₍-₃) and (A₁, D₂₍) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class S construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A₁, A₃) and (A₁, D₄) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S¹ limits of our indices reproduce expected Cardy-like behavior. We will discuss the S¹ reduction of our indices in a separate paper.