Reconstruction of vertex algebras in even higher dimensions

Abstract

Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to dimension one. In the case when D is even, we find natural conditions under which the converse passage is possible. These conditions include a unitary action of the conformal Lie algebra with a positive energy, which is given by local endomorphisms and obeys certain integrability properties.

arXiv comment27 pages; v5 changed the title, fixed typos and improved the exposition

References in corpus (5)

• Vertex Algebras and Algebraic Curves
• Rationality of conformally invariant local correlation functions on compactified Minkowski space
• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Superconformal vertex algebras in four dimensions