Well how do you know what the correct degrees of freedom of QG actually are? Strings seem to tell that you need infinitely many in order to have consistent scattering. It also seems that strings do precisely have the necessary number of degrees of freedom in order to reproduce Bekenstein Hawking Entropy etc. So I see it the other way around, namely that LQG still needs to demonstrate that it can be a consistent approximation/realisation of gravity in the first place.But in contrary to string theory the number of degrees of freedom is finte; no infinite tower of states; simply the final theory. And no additional degres of freedom but the correct degrees of freedom (QCD does not contain mesons as degrees of freedom).
And certainly QCD has mesons as degrees of freedom, in the IR.
Well I do, as do my colleages. This problem can be addressed once one is able to describe scattering processes in LQG. We know that for string theory the intricate structure of the (moduli spaces) of Riemann surfaces is crucial for consistency, ie, unitary scattering. I wonder whether and if so, how, LQG would be able to reproduce this. It may well be, I have no opinion, I am just wondering.I do not see the problem of unitarity.
eg the hierarchy problem, which in a broader sense includes the cosmological constant, is certainly a problem for LQG as well, on top of its intrinsic problems.Not on top; it has different problems. Most (technical) problems we know from QFT, SUSY, SUGRA, ST do not apply to LQG as the theory is formulated differently.
Actually there is more to quantum gravity than UV problems, as certain problems do not depend on the UV completion at all. Moreover it is not even clear whether there are serious UV problems in the first place - due to the phenomenon of classicalization. Some of these issues are going to be discussed here:
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