Jacobi Identity for Vertex Algebras in Higher Dimensions

TL;DR

This paper extends the theory of higher-dimensional vertex algebras by developing formal calculus and polylocal fields, establishing a Jacobi identity that characterizes these algebras and aids in understanding axiomatic quantum field theory.

Contribution

It introduces formal calculus techniques and a Jacobi identity for higher-dimensional vertex algebras, providing a foundational framework for algebraic quantum field theory.

Findings

Derived a Jacobi identity equivalent to the vertex algebra axioms.

Developed formal calculus methods for higher-dimensional vertex algebras.

Investigated the role of polylocal fields in the algebraic structure.

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.