2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94962We 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.40 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 addedHigh Energy Physics - TheoryMathematical PhysicsQuantum Algebratext