Off-topic: a blog of Scientific American: The Simpsons embiggen cromulant papers on string theoryThis text is about Witten's proposal that
There have been various CFT-centered developments here.
First, Jan Manschot (UVA) rewrote the partition sum as an actual sum instead of product, claiming that this form makes it clear that it is a Feynman sum over geometries even though it is not explained too clearly why the individual terms should be interpreted as "geometries".
A week ago, Davide Gaiotto and Xi Yin (HU) have calculated genus two partition sums of these "extremal conformal field theories" or "ECFTs" of Witten. It's an impressive calculation that uses very much the same methods that they know from more conventional compactifications of string theory, further suggesting that neither they nor Witten work on LQG as argued by a supreme crackpot. You should see the formula pi (3.14) on page 9 - the very existence of this solution is a surprise but it exists, in analogy with other stringy miracles. Their methods are effective up to k=10.