Schur indices, BPS particles, and Argyres-Douglas theories

Abstract: We conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional N=2 field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify this conjecture for the special case of free field theories, N=2 QED, and SU(2) gauge theory coupled to fundamental matter. Assuming the validity of our proposal, we compute the Schur index of all Argyres-Douglas theories. Our answers match expectations from the connection of Schur operators with two-dimensional chiral algebras. Based on our results we propose that the chiral algebra of the generalized Argyres-Douglas theory (A_k−1, A_N−1) with k and N coprime, is the vacuum sector of the (k, k + N) W_k minimal model, and that the Schur index is the associated vacuum character.