In Tom Stoer's latest thread, he says "there is growing evidence that the incompleteness of the different approaches [LQG / canonical QGR / spin foams] has a common origin", and suprised suggests that "it may be that trying to quantize an effective theory will never work, ie., without introducing the extra degrees of freedom that are needed for unitarity." This got me thinking: that's a statement about UV completions, can we test it? Well, are there loop-variable quantizations of nongravitational effective field theories, and can we say anything about their UV behavior? But then I thought: loop variables for an ordinary QFT aren't quite the same as LQG; what we really need is a topological QFT. Meanwhile, we usually understand the UV and IR limits of a QFT in terms of a CFT. So the question resolved itself into trying to understand the relationships - the similarities and differences - between LQG, TQFT, and CFT. I haven't looked too hard, but here are two statements I already found. 1) In http://arxiv.org/abs/1010.1939, Rovelli calls his LQG model a generalization of TQFTs as defined by Atiyah. 2) http://arxiv.org/abs/1110.5027 claims to construct a TQFT from CFT. For some reason I don't see anything about CFTs in the paper, but maybe that's in the companion papers. This isn't a pressing topic for me, but I'm just curious what will turn up.