Poisson vertex algebras in supersymmetric field theories

Abstract

A large class of supersymmetric quantum field theories, including all theories with $\mathcal{N}=2$ supersymmetry in three dimensions and theories with $\mathcal{N}=2$ supersymmetry in four dimensions, possess topological-holomorphic sectors. We formulate Poisson vertex algebras in such topological-holomorphic sectors and discuss some examples. For a four-dimensional $\mathcal{N}=2$ superconformal field theory, the associated Poisson vertex algebra is the classical limit of a vertex algebra generated by a subset of local operators of the theory.

30 pages. v2: references added. v3: references added. v4: various improvements; section 3.5 on 3d N=2 SCFTs added; references added; published version

References in corpus (4)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Ω-deformation and quantization
• SCFT/VOA correspondence via $\Omega$-deformation
• Chiral algebras from Ω-deformation

Cited by in corpus (10)

• Feynman diagrams and $\Omega$-deformed M-theory
• Feynman Diagrams in Four-Dimensional Holomorphic Theories and the Operatope
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• Twisted holography of defect fusions
• A domain wall in twisted M-theory
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
• Loop Corrected Supercharges from Holomorphic Anomalies