the correlators need to glue correctly underly composition of cobordisms.
The functionals that satisfy the first of these conditions are called conformal blocks . The second condition is called the sewing constraint on conformal blocks.
So conformal blocks are something like “precorrelators” or “potential correlators” of a CFT.
A. Tsuchiya, K. Ueno, Y. Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Studies in Pure Math. 19, 459–566, Academic Press (1989) MR92a:81191
Kenji Ueno, Conformal field theory with gauge symmetry, Fields Institute Monographs 2008 book page
A.A. Beilinson, Yu.I. Manin, V.V. Schechtman, Sheaves of Virasoro and Neveu-Schwarz algebras, Lecture Notes in Math. 1289, Springer 1987, 52–66
A.Mironov, A.Morozov, Sh.Shakirov, Conformal blocks as Dotsenko-Fateev integral discriminants, arxiv/1001.0563
Conformal blocks for self-dual higher gauge theory are discussed in