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

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.

arXiv comment40 pages. Corrections: changes in the Introduction; added new Remark 4.1; revised Definition 7.1, Proposition 7.1, Remark 8.1 and Proposition 8.2; totally revised Section 9, two Appendices added

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• Globally conformal invariant gauge field theory with rational correlation functions

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