Patrick Hayden points me to hep-th/0410036. If I understand this paper correctly and the paper is correct, this seems to me to be a BIG deal. In this paper, the author take the Hilbert-Palatini action for GR and adds two terms, both of a topological nature. These terms don’t change the fact that the classical theory derived from this action is classical GR. However, the author shows that these terms make this action the same as the action for an so(4,1) [or so(3,2) depending on whether the cosmological constant is positive or negative] Donaldson-Witten topological quantum field theory. The Donaldson-Witten TQFT is an “exactly solvable” quantum theory. What does this mean? Can anyone say a theory of quantum gravity? I knew you could. As the author puts it, “this proves that exact, non-perturbative calculations can be preformed in 3+1 dimensional quantum gravity.”
[Update 10/13/04: Well that was the quick fall. As Nathan Lundblad notes, the paper has been withdrawn!]
O brave new quantum world!
Shame there is no proposal for mass coupling.
“This paper has been withdrawn by the author, due an error in computing the invariance of the so(4,1) and so(3,2) “inner product.”