SCFT/VOA correspondence via $\Omega$-deformation

Abstract

We investigate an alternative approach to the correspondence of four-dimensional $\mathcal{N}=2$ superconformal theories and two-dimensional vertex operator algebras, in the framework of the $\Omega$-deformation of supersymmetric gauge theories. The two-dimensional $\Omega$-deformation of the holomorphic-topological theory on the product four-manifold is constructed at the level of supersymmetry variations and the action. The supersymmetric localization is performed to achieve a two-dimensional chiral CFT. The desired vertex operator algebra is recovered as the algebra of local operators of the resulting CFT. We also discuss the identification of the Schur index of the $\mathcal{N}=2$ superconformal theory and the vacuum character of the vertex operator algebra at the level of their path integral representations, using our $\Omega$-deformation point of view on the correspondence.

arXiv comment22 pages; v2. minor corrections, refs added; v3. minor corrections, refs added, published version

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• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
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• The exact Schur index in closed form
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• Schur sector of Argyres-Douglas theory and $W$-algebra
• Feynman diagrams and $\Omega$-deformed M-theory
• Argyres-Douglas Theories in Class S Without Irregularity
• Poisson vertex algebras in supersymmetric field theories
• A geometric free field realisation for the genus-two class $\mathcal{S}$ theory of type ${\mathfrak{a}}_1$
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Deformation quantizations from vertex operator algebras
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Comments on chiral algebras and $\Omega$-deformations
• A domain wall in twisted M-theory
• 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
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Lectures on chiral algebras of $\mathcal{N}⩾2$ superconformal field theories
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Structure of the $\mathcal{N}=4$ chiral algebra