Schur correlation functions on $S^3\times S^1$

Abstract

The Schur limit of the superconformal index of four-dimensional $\mathcal{N}=2$ superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra. Applying localization techniques to the theory suitably put on $S^3\times S^1$, we obtain a direct derivation of this fact. We also show that the localization computation can be extended to calculate correlation functions of a subset of local operators, namely of the so-called Schur operators. Such correlators correspond to insertions of chiral algebra fields in the trace-formula computing the supercharacter. As a by-product of our analysis, we show that the standard lore in the localization literature stating that only off-shell supersymmetrically closed observables are amenable to localization, is incomplete, and we demonstrate how insertions of fermionic operators can be incorporated in the computation.

arXiv comment49 pages

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• $\mathcal{N}=2^{\ast }$ Schur indices
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• Schur sector of Argyres-Douglas theory and $W$-algebra
• Argyres-Douglas Theories in Class S Without Irregularity
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• More on holographic correlators: Twisted and dimensionally reduced structures
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Surface defects, flavored modular differential equations and modularity
• One-Dimensional Sectors From the Squashed Three-Sphere
• Giant gravitons in twisted holography
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Closed form fermionic expressions for the Macdonald index
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Deformation quantizations from vertex operator algebras
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Intersecting Surface defects and 3d Superconformal indices
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Schur correlation functions from q-deformed Yang-Mills