Is there some hint of susy in LQG?

[arivero]

Point is, Huerta and Baez, building upon the shoulders of M-theoretists, show us that susy is more relevant that just a trick to move the dimension of string theory. And Bott periodicity in Connes models did the same hint. Still, it seems that besides sugra, no model of space time has been able to formulate susy in a natural way.

What about LQG? With so much thinking about fermions, superspace should be something natural, but is it?

 

[marcus]

Arivero, interesting question! I assume you know of Thiemann's 2011 papers about supersymmetry in LQG.
But in case not, or in case other readers are curious, I will give links.
There were several talks about this work at the May Loops 2011 conference in Madrid. He did the work with a couple of his Erlangen PhD students, Thurn and Bodendorfer. I will also list some papers that are not directly SUGRA but deal with doing LQG in higher dimensions...

3. arXiv:1106.1103 [pdf, ps, other]
Towards Loop Quantum Supergravity (LQSG)
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 12 pages

4. arXiv:1105.3710 [pdf, ps, other]
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 12 pages

5. arXiv:1105.3709 [pdf, ps, other]
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 43 pages

7. arXiv:1105.3706 [pdf, ps, other]
New Variables for Classical and Quantum Gravity in all Dimensions IV. Matter Coupling
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 13 pages

8. arXiv:1105.3705 [pdf, other]
New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 34 pages

9. arXiv:1105.3704 [pdf, other]
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 43 pages

10. arXiv:1105.3703 [pdf, other]
New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn
Comments: 28 pages

 

[atyy]

Livine and Ryan also worked on supersymmetry in LQG.
http://arxiv.org/abs/0710.3540
http://arxiv.org/abs/1004.0672

 

[marcus]

Caveat: unfortunately I cannot answer your question about the naturalness of SUSY in LQG. You might be able to get some inkling of an answer for yourself by glancing at these papers. Or someone else, like Atyy or Tom Stoer, may be able to offer an opinion.

I only spent a short time on the Thiemann papers and cannot recommend or comment. Can only give links to them for whoever wants to dig deeper.

 

[arivero]

I had not read Thiemann's initiative. Let's see where it goes. I remember a false start in NCG, where Frölich and his students tryied to build susy into the spectral triples.

As the first works from Baez and Huerta Huerta say, a key piece is triality, and with triality then it comes all the family D=3,4,6,10. Thiemann goes too far if it is able to work in any number of dimensions, he should exhibit at some moment a natural -abused word- way of constraining the possibilities to this set, or signatures s=1,2,4,8.

For instance, it could be interesting to see how/if something similar the bypass of Chung and Sudbery (http://inspirehep.net/record/22268/?ln=es), replacing complex by octonions, allows to jump from the four dimensional LQG to some ten dimensional LQG. I note that recent work of Baez is still rumiating about this kind of replacements, perhaps he could be attracted to LQG??

 

[arivero]

Let me add some references on the complicated relationships between division algebras and supersymmetry. Of course there are some attempts from time to time, and most of us can call Adler, or Dixon, or our favorite outsiders. Perhapse the earlier attempt is Murat Günaydin and Feza Gürsey "Quark structure and octonions", which dates from 1973. These authors keep playing in the susyfication of the algebras.


But first article full on the topic seems to be Nov 1982 Supersymmetry and the division algebras by Kugo and Townsend (Journal). I note that a bit later, in Dec 1983, there is a not completely unrelated colaboration between Gunaydin, Sierra, and Townsend about "Exceptional Supergravity Theories and the MAGIC Square". You can remember a more recent Sierra-Townsend collaboration, on "Landau levels and Riemann zeros". It is amusing that Connes did also a similar try nearly at the same time.

The topic sleeps for five years, it is touched here and there (Fairlie and Manogue 1986, e.g.), and then it flourishes :
10 July 1987 Gürsey on "Super Poincaré Groups and Division Algebras"
3 August 1987. we have Chung, A. Sudbery aforementioned work.
In Oct 9, 1987 J.M. Evans Supersymmetric Yang-mills Theories And Division Algebras.
And then still in 1988. Foot and Joshi "On a Certain Supersymmetric Identity and the Division Algebras" and Kimura and Oda views of the "Brink-Schwarz superparticle", with http://ptp.ipap.jp/link?PTP/80/1/ and -with Nakamura- http://ptp.ipap.jp/link?PTP/80/367.

After this, the topic has been scarcely revisited (Manogue, Evans, etc); it has become just a piece of M-Theory, on the grounds of the Brane Scan. There is some missing piece, perhaps related to 11 dimensions, Hopf fiberings and Kaluza Klein. We have discussed on it elsewhere. The point here is that a sucessfull attempt to put susy into LQG should reveal some overplus structure up to 10 or 11 dimensions, and this structure should be, one hopes, the (standard model) particle content.

 

[mitchell porter]

this structure should be, one hopes, the (standard model) particle content.

Rios and Sheppeard, via Brannen, have tried to get the SM by directly employing exceptional algebras, in a context that at least resembles LQG - I just wrote up a description. It's noteworthy because they also try to use Bilson-Thompson's braids! - Sheppeard looks to embed the relevant braid algebra in Rios's matrix models.

Another link between supersymmetry and the division algebras can be found in this talk by David Tong (part 2, slides 27 and 28); something to do with Berry phases. I can't explain it, but I'll point out that this work by Tong has some resemblance to entropic gravity 2.0, the version which now talks about adiabatic reaction forces rather than an entropic force. Also, Rios's papers from 2005, clearly inspired by Lee Smolin's attempt to derive M-theory, might be worth a look. One is an LQG paper, while the other reminds me of Heckman and Verlinde's recent effort.

 

[arivero]

Another link between supersymmetry and the division algebras can be found in this talk by David Tong (part 2, slides 27 and 28); something to do with Berry phases. I can't explain it, but I'll point out that this work by Tong .

Great! I did not notice this work by Tong; he is one of the young promises of the field and here it is proven that he really likes his work. About october or november 2006, a student (not me!), during the routine QFT lectures, caught him off guard by asking about the implications of Hopf maps when trying to build a basis which is non zero everywhere. Two years later, it is not only that he has refreshed his memory... he has even being able to contribute to the topic!