Deformation quantizations from vertex operator algebras

Abstract

In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. We answer this question positively if the UV R-symmetries do not mix with accidental (topological) symmetries along the renormalization group flow from the four-dimensional theory on a circle to the three-dimensional theory. If they do mix, we still find a deformation quantization but at different values of its period.

arXiv comment40 pages; v2: argument in section 4.1 refined, references added; v3: minor improvements, published version

References in corpus (34)

• Infinite Chiral Symmetry in Four Dimensions
• The Exact Superconformal R-Symmetry Extremizes Z
• Gauge Theories and Macdonald Polynomials
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• W Symmetry in six dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• Correlation Functions of Coulomb Branch Operators
• Chiral algebras of class S
• Deformation quantization and superconformal symmetry in three dimensions
• Stress-tensor OPE in N=2 Superconformal Theories
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Chiral Algebras for Trinion Theories
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• VOAs labelled by complex reflection groups and 4d SCFTs
• High-temperature asymptotics of supersymmetric partition functions
• On 4d rank-one N=3 superconformal field theories
• sl^(2)_{-1/2}: A Case Study
• Current Algebra on the Torus
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Macdonald Index and Chiral Algebra
• N=2 S-duality Revisited
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Free Field Realizations from the Higgs Branch
• Schur correlation functions on $S^3\times S^1$
• SCFT/VOA correspondence via $\Omega$-deformation
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Chiral algebras from Ω-deformation
• A tale of exceptional 3d dualities
• Chiral Algebras, Localization and Surface Defects
• Flavor symmetries and unitarity bounds in $\mathcal{N}=2$ SCFTs
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Testing Macdonald Index as a Refined Character of Chiral Algebra

Cited by in corpus (7)

• The exact Schur index in closed form
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Surface defects, flavored modular differential equations and modularity
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• Intersecting Surface defects and 3d Superconformal indices
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Schur correlation functions from q-deformed Yang-Mills