On p. 13 of "Vertex Algebras for Beginners", 2nd edition, Kac writes:

"Under certain assumptions and with certain additional data one may reconstruct the whole QFT from these chiral algebras, but we shall not discuss this problem here".

However, he does not give any references to support this claim (at least not next to the claim) and I was not able to find any on my own.

Does anybody know of any references?