# SUSY and SUGR in spin foam

1. Oct 18, 2007

### marcus

New paper out today about supersymmetry in spin foam QG
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 identify positively 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=2 loop 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)

Last edited: Oct 19, 2007
2. Oct 19, 2007

### Chronos

I view that as a retreat from earlier papers. Not that it is a bad thing, merely an acknowledgement that prior conjectures may have been too bold, IMO.

3. Oct 19, 2007

### marcus

Hi Chronos,

the main belief in SUSY was back in the 1990s, or so I'm told. Regularly, almost on an annual basis, important string people would announce that SUSY was about to be observed. It was just around the corner (in a lot of people's minds.)

Compared with earlier, there is now not so much belief in SUSY or concern with it AFAICS---except that stirred up by the approach of colliderday picnic. My view anyway.

I think the main papers implicating spinfoam with SUSY date from 1999-2000, back when SUSY probably seemed like a realer prospect to more people. I will get the abstracts so we can have a look.

http://arxiv.org/abs/hep-th/9904016
Supersymmetric Spin Networks and Quantum Supergravity
Yi Ling, Lee Smolin
21 pages, 22 figures
(Submitted on 2 Apr 1999)

"We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative quantization of supergravity. The supersymmetric extension of the area operator is defined and partly diagonalized. The spectrum is discrete as in quantum general relativity, and the two cases could be distinguished by measurements of quantum geometry."

http://arxiv.org/abs/hep-th/0009020
Introduction to supersymmetric spin networks
27 pages, 16 figures. Based on the talk given at Marcel Grossmann Meeting IX in Rome
Yi Ling
(Submitted on 3 Sep 2000)

"In this paper we give a general introduction to supersymmetric spin networks. Its construction has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a special kind of spin networks with superalgebra Osp(1|2n). It turns out that the set of corresponding spin network states forms an orthogonal basis of the Hilbert space $$\cal L\mit^2(\cal A\mit/\cal G)$$, and this argument holds even in the q-deformed case. The Osp(n|2) spin networks are also discussed briefly. We expect they could provide useful techniques to quantum supergravity and gauge field theories from the point of non-perturbative view."

http://arxiv.org/abs/hep-th/0003285
Eleven dimensional supergravity as a constrained topological field theory
Yi Ling, Lee Smolin

Last edited: Oct 19, 2007
4. Oct 19, 2007

### ensabah6

I recall "Robert Oeckl" publishing SUSY + SF extensions, I've wondered if adding SUSY improves SF's semiclassical behavior, and whether Smolin's current work can be accommodated in some way.

5. Oct 20, 2007

### Chronos

Just for the record, Marcus. I believe the LHC will yield unexpected results, but not SUSY.

6. Oct 20, 2007

Why not?