New paper out today about supersymmetry in spin foam QG(adsbygoogle = window.adsbygoogle || []).push({});

Spin foam is the leading non-string approach to quantum gravity in the Loop community---in the sense of currently having the most people working on it and the most papers. Maybe quantum cosmology is on par--I didnt make a careful count. But I think not. Spinfoam has a large part of the non-string QG research action in any case.

So it's interesting to know how SUSY would fit into the spinfoam picture. And that is what this new paper of Livine and Ryan indicates.

http://arxiv.org/abs/0710.3540

N=2 supersymmetric spin foams in three dimensions

Etera R. Livine, James P. Ryan

12 pages

(Submitted on 18 Oct 2007)

"We construct the spin foam model for N=2 supergravity in three dimensions. Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has representations which are not completely reducible. This complicates the procedure when building a state sum. Fortunately, one can and should excise these representations. We show that the restricted subset of representations form a subcategory closed under tensor product. The resulting state-sum is once again a topological invariant. Furthermore, within this framework one can identifypositively and negatively charged fermions propagating on the spin foam. These results on osp(2|2) representations and intertwiners apply more generally to spin network states for N=2loop quantum supergravity (in 3+1 dimensions)where it allows to define a notion of BPS states."

Some of the QG approaches that I personally find most interesting predict in effect NO-susy and NO-extra dimensions. So they are falsifiable by LHC. If LHC sees susy or extra dimensions they are dead. for instance I do not see how Smolin ball-and-tube model with the Sundance standard model could survive either of those findings, and I think that's a good thing. A real theory predicts something definite---which puts it at risk.

But just because some of the most exciting QG approaches predict NO-susy (assuming I am correct about this) does not mean that ALL nonstring QG approaches do so. And in fact it looks as if the popular spinfoam approach can assimilate SUSY very well.

So that is something to at least register: even if SUSY has failed repeatedly to be discovered. It is still a logical possibility (if remote) that it could be discovered, and this is how spin foam could accomodate it.

Livine and Ryan cite several earlier papers on supergravity and supersymmetry spin foam by Yi Ling and Lee Smolin. This line of research goes back to year 2000. They also mention a forthcoming paper--their reference [15]

[15] E.R. Livine and J.P. Ryan, Spinfoam Supergravity in 3d, (to appear) ...we need to solidify our reasoning with an analysis of the pertinent semi-classical limit. This will be the subject of later work [15]. We shall develop a connection between the model developed here and fermionic fields coupled to gravity in the arena of Regge calculus.

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# SUSY and SUGR in spin foam

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