Reconstruction of a vertex algebra in higher dimensions from its one-dimensional restriction

Bojko Bakalov, Nikolay M. Nikolov

Published 2022-09-06Version 1

Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in higher dimensions admits a restriction to a vertex algebra in any lower dimension, and in particular, to dimension one. In this paper, 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.