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?



The proof that a vertex algebra can lead to a Wightman QFT
I found Nikolov's paper "Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory" [arXiv:hep-th/0307235](https://arxiv.org/abs/hep-th/0307235). The abstract:



> 
> We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. An one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT) with global conformal invariance (GCI) is constructed. 
> 
> 
> 


Now he did not explicitly show how are these generalized vertex algebras related to the usual chiral vertex algebras. So in my master's thesis  [arXiv:1607.05078](http://arxiv.org/abs/1607.05078) I restricted myself to unitary (quasi-)vertex operator algebras and reversed Kac's proof.


