Monday, June 25, 2007

Witten's monstrous paper is out

It has 82 pages. The previous blog text about the topic was
Monstrous symmetry of black holes.
Properties of the CFTs dual to pure AdS3 are considered. The allowed central charges are identified. The discussion of the Chern-Simons description may look a bit overblown given the fact that this description can't be made non-perturbatively exact in any known way.

The monster symmetry of the minimum choices is supported by numerology based on the dimensions of irreps of the monster group and applied to some partition sums - I have almost no doubt that the conclusion of this numerology is correct - but the dimensions of the irreps seem to be the only property of the monster group that is ever used which I find somewhat disappointing: someone else will have to find something more about the importance of the monster group and its rich properties in this gravitational setup later.

And that's the memo.

Graviweak unification

I was also intrigued by two papers by Fabrizio Nesti who is incidentally also the author of the JHEP LaTeX macro. The second of these papers was written with Roberto Percacci. Unfortunately, the excitement lasted for 140 seconds only (and that's more than it would be otherwise because I have looked at it with a 56k modem).

They want to unify the Lorentz group with the gauge group - namely a Pati-Salam group - using some magic with spinors. Well, this seems to violate the Coleman-Mandula theorem. They make a funny argument that the theorem doesn't apply because the Lorentz indices are internal - this argument is complete nonsense, as far as I can say (if this loophole existed, one could always use it to humiliate Coleman and Mandula) - and what they have is only a pure bookkeeping device how to organize all the spinor components. There is no sign of genuine unification of gravity with the gauge forces here, for example a unification of the Einstein-Hilbert action with the Yang-Mills action.

I think that all such methods to unify must look like Kaluza-Klein theory or a different limit of string theory. Everyone who has proposed any other logic that "also" unifies the forces - including Alain Connes - is confused about some pretty elementary facts about the identity of forces, the different roles of groups in physics, and about the meaning of the word "unification".

And that's another memo. :-)

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