Reconstruction of vertex algebras in even higher dimensions

TL;DR

This paper explores the conditions under which higher-dimensional vertex algebras can be reconstructed from lower-dimensional ones, focusing on even dimensions and conformal invariance in quantum field theory.

Contribution

It establishes natural conditions for reconstructing even-dimensional vertex algebras from lower-dimensional cases, involving unitary conformal actions and integrability.

Findings

Reconstruction is possible under specific conditions in even dimensions.

Unitary conformal actions with positive energy are key to the reconstruction.

Provides a framework linking higher and lower-dimensional vertex algebras.

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.