Constructions of vertex operator coalgebras via vertex operator algebras

The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions modeling one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that any vertex operator algebra equipped with a nondegenerate, Virasoro preserving, bilinear form gives rise to a corresponding vertex operator coalgebra. We then explicitly calculate the vertex operator coalgebra structure and unique bilinear form for the Heisenberg algebra case, which corresponds to considering free bosons in conformal field theory.