What are Tom Banks's arguments against a QFT of quantum gravity? https://arxiv.org/abs/1007.4001
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What are his arguments here against a QFT of QG, can someone provide a simpler explanation of these?
 And to what specific theories of QG do these arguments apply to?
 A: Gravity is not renormalizable in four dimensions. The entire idea of formulating gravity as QFT in four dimensions rests on the fact that whether one can actually find an interacting fixed point in UV such that based on experiments, one can fine-tune finite (and small) number of parameters to define a consistent QFT. This possibility was put forward by Weinberg in the 1970s. This is now known as 'asymptotic safety'. If gravity is indeed asymptotically safe, then one expects a fixed point in the UV (small scales) around which the theory behaves like a conformal field theory (CFT). For a CFT, one expects that entropy will go as, $\sim S ∼ E^{(d-1)/d}$ [See https://arxiv.org/abs/0709.3555]. In GR, the entropy goes as, $\sim S ∼ E^{(d-2)/(d-3)}$. They are different scalings for any integer $d$. The author notes - "It, therefore, follows that the large energy asymptotics of the density of states in a theory of gravity in asymptotically flat spacetime is not that of any conformal field theory, and therefore, it is not a renormalizable quantum field theory". This paper mentions that this result was initially discussed by Banks and Aharony in https://arxiv.org/abs/hep-th/9812237. This is the summary (simplest) of Banks's argument.  
