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 (A(1), A(2n-3)) and the(A(1), D-2n) 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 (A(1), A(2n-3)) and (A(1), D-2n) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class. construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A(1), A(3)) and (A(1), D-4) 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 S-1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S-1 reduction of our indices in a separate paper.