Abstract
We construct the wave functions in the $q$-deformed 2D Yang-Mills theory that compute torus correlation functions of affine currents in the vertex operator algebra associated to a class of 4D $\mathcal{N}=2$ superconformal field theory. These wave functions are then shown to reduce to the topological correlators of a set of Coulomb branch operators in the $T[SU(N)]$ theory, from which those correlators in the 3D mirror dual of the 4D ${T}_{N}$ theories can be computed.
Highlights
Four dimensional N 1⁄4 2 superconformal field theory (SCFTs) are found to contain a privileged class of operators, referred to as the “Schur operators,” endowed with a vertex operator algebra (VOA) structure [1]
The R symmetry of the 4D theory guarantees the presence of a Virasoro subalgebra, while any flavor symmetry g enhances to an affine algebra gk, whose generators descend from the flavor moment maps in 4D
The aim of this article is to propose a parallel approach to computing some of these correlators, by constructing the wave functions corresponding to the affine current operators for a class of 4D SCFTs of class S of type g, and show that they are determined by the correlators of critical current algebras
Summary
Four dimensional N 1⁄4 2 superconformal field theory (SCFTs) are found to contain a privileged class of operators, referred to as the “Schur operators,” endowed with a vertex operator algebra (VOA) structure [1]. Correlation functions of Schur operators on the torus are computed via supersymmetric localization [7,8] and are further mapped to the deformation quantization of the Higgs branch of vacua [9,10,11,12,13,14] of the circle-reduced theory in 3D. The aim of this article is to propose a parallel approach to computing some of these correlators, by constructing the wave functions corresponding to the affine current operators for a class of 4D SCFTs of class S of type g, and show that they are determined by the correlators of critical current algebras. We will relate the dimensionally reduced wave functions for the TN theories with the Coulomb branch correlators in the 3D mirror dual [15,16], namely, the star-shaped quiver gauge theories. We discuss the possible generalization to other T1⁄2G theories
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