The paper you are referring to is:
http://arxiv.org/abs/hep-th/0501191
Date (v1): Mon, 24 Jan 2005 17:29:34 GMT (18kb)
Date (revised v2): Wed, 9 Feb 2005 22:07:06 GMT (18kb)
Quantum gravity in terms of topological observables
Authors: Laurent Freidel, Artem Starodubtsev
Comments: 19 pages
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely small 10^{-120}. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory.
In my view what has been happening, and given that we're only in April, I'm really looking at the past couple of years into 2003, is that LQG is leaving the toy model stage and becoming a genuine theory of gravity about which one can draw conclusions.
Y-M in 2D just doesn't cut it for all but the diehards. But, in Alexander's paper, you have him actually presenting a pretty well full fledged set of equations that can operate in the four dimensional reals and drawing conclusions from it. Freidel likewise in looking at LQG is putting together a formulation that you can actually do something with and making real predictions. Deur, who I cite above for a brief paper (and he hasn't published anything else) starts to draw some conclusion, in general, about how any non-abelian gauge theory of gravity is going to differ from conventional GR in the real world.
The paper you cited a few weeks ago about the rank 2 gravitational tensor S in quantum gravity not being identical to the corrosponding one in GR does the same thing. Likewise, the slightly older paper which made the point that SF naturally leads to an emergent 4D without putting it in by hand is a big deal. These theories are starting to be real theories that be used to draw conclusions, instead of mere works in process from which we can make vague hunches.
As LQG has "gone real" the analogies to QCD have grown a lot more relevant. It is one thing to look at a generalized Y-M in 2D or some such. But, when your gravity equations and your QCD equations start to look similar and this allows you to use real empirical QCD experience to back up your analytical judgment about what LQG equations say, you have started to jump the shark. Also, the more similar gravity begins to look to QCD, and Alexander's paper's theta notation really brings the parallel to a new level of specificity, the most you are inclined to speculate that they aren't just similar or roughly analogous, but are part of the same thing.
Now, it isn't obvious to me that QCD relies very heavily a preferred frame or any other non-GR features, even if, more out of laziness than anything else, non-GR elements may not be throughly stamped out. QCD involves such local phenomena in any case that it seems as if it would take a lot of local distortion in spacetime for GR geometrical issues to be very relevant to QCD.
Mass is a bigger issue. Y-M doesn't like mass. Hence, the call for the Higgs. As you are no doubt aware, the bulk of Baez's "fundamental constants" are Higgs related. And, of course, any theory of gravity is fundamentally about mass. I don't have a lot of confidence that LHC is going to find a Higgs boson, although I'd love to be proven wrong. At any rate, I do think that the whole issue of mass is pretty much up in the air until experiment catches up in the form of LHC that either say that there is a Higgs boson that fits or that somebody got it wrong.
Now, of course, you know that I'm a big MOND fan, and I think that the cool part of developments like those of Alexander's paper and Deur's and the paper that says that while quantum gravity implies a rank 2 tensor for gravity that it does not imply the one in GR, is that a MOND-TeVeS type theory which is theoretically motivated by falling naturally out of a quantum gravity equation makes the case for a sensible universe without dark matter, without dark energy, without lots of extra dimensions, etc. much more plausible. Indeed, it would be a wonderful gap filler. From the empirical evidence, you get a toy model theory with the constants filled in, and from the theory, you get an exact formula theory with no constants, and I think you can then reconcile the two to have not just a toy model, but a theoretically well motivated exact formulation whose constants are well measured empirically.
Now, this is still fuzzy about how this is all going to knit together and unify, i.e. how the QCD is going to become the flip side of gravity, instead of just similar to it. But, basically, a paper like Alexander's makes the analogy start to get sufficiently tight that my intuition is saying, maybe it can be knit a bit tighter. But, I think that you don't really get to that level until you get more solid in the "All the Constants from . . . " line of analysis and connect the plausible empirical formulas to some sort of theoretical foundation that tells you more about what the particles of SM really are.
(Apologizes for being lazy and leaving out of lot of links in this post to the relevant papers and sites, I do have a day job).
)