Superconformal Index, BPS Monodromy and Chiral Algebras

Abstract

We show that specializations of the 4d $\mathcal{N}=2$ superconformal index labeled by an integer $N$ is given by $\text{Tr}{\mathcal{M}}^N$ where $\mathcal{M}$ is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras ${\mathcal{A}}_N$. This generalizes the recent results for the $N=-1$ case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on $S^2\times T^2$ where we turn on $\frac{1}{2}N$ units of $U(1{)}_r$ flux on $S^2$.

91+2 pages, 4 figures; v2 references added

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Cited by in corpus (8)

• Chiral algebra of Argyres-Douglas theory from M5 brane
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• On Irregular Singularity Wave Functions and Superconformal Indices
• Macdonald Index and Chiral Algebra
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• Orbifold Schur Index and IR formula