Schur indices, BPS particles, and Argyres-Douglas theories

By Clay Córdova, Shu-Heng Shao. 2015

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A bstractWe conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional N=2$$ \mathcal{N}=2 $$ 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$$ \mathcal{N}=2 $$ 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 (Ak−1, AN−1) with k and N coprime, is the vacuum sector of the (k, k + N) Wk minimal model, and that the Schur index is the associated vacuum character.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ee194facce2c9daf06305c50bfcdfa9833ba5c79