Existence of pure quantum gravity

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atyy

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Baez says that it was Witten who showed the relationship between the Turaev Viro spin foam model and gravity. http://math.ucr.edu/home/baez/week15.html

It's amazing how much LQG is based on Witten's (misleading?) ideas. Despite the problems mentioned in the link mitchell porter gave above, he is still writing papers about Chern-Simons theory and gravity. http://arxiv.org/abs/1001.2933
 
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Possibly John Baez is referring to http://inspirebeta.net/record/264816?ln=en". This paper by Witten from 1988 is reference 6 in 2007's "Three-dimensional gravity revisited", and he begins there by criticizing his own views from 1988.

Meanwhile, see Barrett and Naish-Guzman's review on http://arxiv.org/abs/0803.3319" [Broken], page 4: "Witten’s quantum gravity with a cosmological constant is known to be equivalent to the Turaev-Viro model, since both are the square of an SU(2) Chern-Simons theory" - and here two papers are cited, one of them Witten 1988.

That whole paragraph on page 4 of B&NG, and also section 7, would appear to be very useful in making the critical comparison between T-V and Witten's AdS3 - because B&NG make statements about the properties of 2+1 gravity with positive and with zero cosmological constant, while what I've called "Witten's AdS3" is 2+1 gravity with negative cosmological constant. But if we consult Witten 2007, he says he doesn't know how to do quantum gravity with positive cosmological constant (for more, see his http://arxiv.org/abs/hep-th/0106109" [Broken]).

So I think we have arrived at the place where we can make the comparison. We have here models of 2+1 gravity for the three basic cases - spherical, flat, and hyperbolic geometry. But the author of the model of 2+1 gravity in hyperbolic space (Witten 2007) claims that his earlier work (Witten 1988) was incomplete, and this earlier work indirectly motivates or justifies the models for spherical space and flat space (Barrett & Naish-Guzman 2008). Nonetheless, the approach to quantum gravity in Witten 2007 is not wholly disconnected from that in Witten 1988; Chern-Simons theory is still playing a role; the new approach is supposed to be an improvement. Meanwhile, Barrett & Naish-Guzman advance their own philosophy of how to think about 2+1 gravity in some detail, in a way that is implicitly consistent with Witten 1988. There has to be ample material here from which we can learn something.
Looking at the thread you linked to, it seems Witten's conjecture is wrong. So there is no known definition of pure 3D quantum gravity in AdS.
That's not quite it. Witten conjectured the existence of a series of such theories, each possessing monster-group symmetry on the boundary. Gaiotto proved that the second conjectured theory in that series can't exist, but the first theory does exist, and there may be higher theories in the series with a smaller symmetry group.
 
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