The previous review of loop quantum gravity was discussed here. Some of my objections to loop quantum gravity are listed here.
A new brief review of loop quantum gravity by Nicolai and Peeters appeared yesterday. They show all the nice things that many of us have been attracted by for several weeks (and some slower people are attracted by for several decades), especially the discrete spectrum of areas. The key point they emphasize is that the main problem of quantum gravity is the infinite number of coefficients of higherderivative terms that are undetermined, making the theory completely unpredictive. They show that this infinite unpredictivity is, in the context of loop quantum gravity and spin foams, just translated into the infinite number of unknown parameters of the Hamiltonian or the spin foam rules.
This implies that loop quantum gravity and its variations make zero (0) progress in solving any problems of quantum gravity.
Nicolai and Peeters also argue that there is an important difference between lattice gauge theories and latticized general relativity. In the first case, one can independently take the continuum limit and the classical limit (lattice QCD). In the latter case, it is not possible, despite the (wrong) assumption of all the people who promote loop quantum gravity. Nicolai and Peeters use the fact that no physical semiclassical state has been found in loop quantum gravity which shows that the assumption is probably wrong.
I think that there is a more straightforward and reliable way to argue that this assumption of loop quantum gravity about the independent limits is patently false. The classical limit and the continuum limit in quantum gravity is the same thing simply because the "dynamical lattice spacing" is proportional to the square root of Planck's constant (recall the formula for the Planck length). Taking the Planck's constant to zero is therefore equivalent to taking the lattice spacing to zero. QED.
In other words, diffeomorphisms which must be a symmetry of quantum gravity allow us to convert a large coordinate distance into a small coordinate distance with a smaller value of Planck's constant, and therefore, these two limits cannot be considered separately (and the continuum limit cannot be taken as a separate step after the quantization). This is of course nothing more than the 487th argument that kills loop quantum gravity.
The 488th argument that they repeat is ultralocality  the inability to obtain the usual concepts of continuity of space from loop quantum gravity which is equivalent to the nonseparability of the kinematical Hilbert space.
Comments of the Week #154: from Earth as seen from the Moon to the Universe at its birth

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22 hours ago
snail feedback (1) :
Dear Lubos,
'... it is thus perhaps best to view spin foam models ... as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clearcut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semiclassical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.'  Page 14 of http://arxiv.org/abs/hepth/0601129
The reason for the technical problems like an infinite number of potential solutions is simply a lack of connection to reality. This is the same problem which stops string theory from succeeding after 20 years of intense funding, which LQG has not had!
I don't think the aim of science is just to link GR and QFT by some kind of mathematical fiddle of the Feynman path integral, but the broader picture of understanding why gravity is so much weaker, and being able to predict it.
The conventional aim of producing a theory that "predicts gravity" by merely being consistent with unobserved hypothetical spin 2 graviton conjectures is no good.
Maxwell fiddled his theory to fit the facts, but at least his equations allow me to calculate electromagnetic phenomena.
With both string theory and LQG you have a mathematically far more complex and incomplete version of something like Maxwell's aether electromagnetism, but the equations are useless for practical things. You can't calculate Standard Model parameters with them, or anything.
So you are left with the physical picture  10/11 dimensional strings and 10^500 vacuua. This is why I think LQG spin foam vacuum is more realistic  it is tied to reality.
It's a pity you people are so constrained to only seeing abstract mathematical approaches and technical details of speculative conjectures. Top physicists should be resolving the reasons why Maxwell's equations wrongly predict continuous and not discrete electromagnetic waves for atomic phenomena. Once this is sorted, then you will a correct model for one observable unified force (electromagnetism) which will be a foundation for getting a grasp of quantum gravity. At present, anomalies between real observed physics phenomena and the mathematical models are swept under the carpet. And some people have the cheek to speculate on SUSY and other unobservables.
Nigel
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