  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.
