Reconstruction of vertex algebras in even higher dimensions
arXiv:2209.02421 · doi:10.1007/s00023-023-01384-0
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.
27 pages; v5 changed the title, fixed typos and improved the exposition