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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.
Córdova et al. (2016) studied this question.