Jacobi Identity for Vertex Algebras in Higher Dimensions
arXiv:math-ph/0601012 · doi:10.1063/1.2197687
Abstract
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.
35 pages, references added
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Cited by in corpus (12)
- W-Constraints for the Total Descendant Potential of a Simple Singularity
- Twisted logarithmic modules of vertex algebras
- Harmonic bilocal fields generated by globally conformal invariant scalar fields
- Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
- Perturbative Quantum Field Theory via Vertex Algebras
- Conformal field theories with infinitely many conservation laws
- Infinite dimensional Lie algebras in 4D conformal quantum field theory
- Pole structure and biharmonic fields in conformal QFT in four dimensions
- Superconformal vertex algebras in four dimensions
- Semi-Differential Operators and the Algebra of Operator Product Expansion of Quantum Fields
- Toroidal vertex algebras and their modules
- Reconstruction of vertex algebras in even higher dimensions