Quote by marcus
Personally I am not sure about the precise relation of the CraneYetter model (a topological quantum field theory) to quantum gravity.

Alexandrov explains this in detail.
It's not about the relation between CY and QG; it's about the quantization method.
Alexandrov shows that using the EPRL and FK method in case of the CY model explicitly gives us a wrong result (there are several ways to derive the CY model, so the SF rep. is wellknown); then he uses a different method to implement the constraints (Dirac + deltafunction in the measure) and he finds the correct CY vertex.
So the conclusion is that the method used by EPRL and FK is wrong.