Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory

TL;DR

This paper extends the concept of vertex algebras to higher dimensions and establishes a correspondence with globally conformal invariant quantum field theories, advancing the mathematical framework of conformal QFT.

Contribution

It introduces a new definition of vertex algebras in arbitrary space-time dimensions and links them directly to GCI quantum field theories.

Findings

Established a one-to-one correspondence between higher-dimensional vertex algebras and GCI QFT.

Extended vertex algebra theory beyond two dimensions.

Provided foundational structure for conformal quantum field theories.

Abstract

We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. An one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT) with global conformal invariance (GCI) is constructed.