Another installment by John Baez on the September 2008 Corfu QG School.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks to MTd2 for noticing this and supplying the link.

There is a part that is so informative we should have a brief excerpt to look at closely:

==quote Baez==

...

...But now - on to Corfu!

Last time I said a bit about what I learned in Ashtekar and Rovelli's courses. Now I'd like to talk about some other things I learned in Corfu - some things I find even more tantalizing.

In "week232", I explained how gravity in 3d spacetime automatically contains within it a theory of point particles, and how a 4d analogue of 3d gravity automatically contains within it a theory of string-like objects. This 4d theory is called BF theory. Like 3d gravity, it describes a world where spacetime is flat. So, it's boring compared to full-fledged 4d gravity - so boring that we can understand it much better! In particular, unlike 4d gravity, we understand a lot about what happens when you take quantum mechanics into account in 4d BF theory.

But when you remove a surface from spacetime in 4d BF theory, it springs to life! In particular, the surface acts a bit like the worldsheet of a string. It doesn't behave like the strings in ordinary string theory. But Winston Fairbairn has been thinking about this a lot:

17) Winston J. Fairbairn and Alejandro Perez, Extended matter coupled to BF theory, Phys. Rev. D78:024013, 2008. Also available as arXiv:0709.4235.

18) Winston J. Fairbairn, On gravitational defects, particles and strings, JHEP 0809:126, 2008. Also available as arXiv:0807.3188.

19) Winston J. Fairbairn, Karim Noui and Francesco Sardelli, Canonical analysis of algebraic string actions, available as arXiv:0908.0953

And it turns out that if we impose the constraints on BF theory that turn it into general relativity, we obtain the usual Nambu-Goto string, where the action is the area! However, the last of the three papers above shows there are some subtle differences.

I need to think about this a lot more. It was always my hope to reconcile string theory and loop quantum gravity, and this could be the way. Of course, reconciling two things that don't work doesn't necessarily give one that does. A pessimist might say that combining string theory and loop quantum gravity is like combining epicycles and aether. But I'm optimistic. Something interesting is going here.

In a different but possibly related direction, Aristide Baratin gave a talk on recent work he's been doing with Derek Wise and Laurent Freidel. You can get a feel for this work from this paper:

20) Aristide Baratin, Derek K. Wise, 2-Group representations for spin foams, to appear in proceedings of the XXV Max Born Symposium: The Planck Scale, Wroclaw, Poland. Also available as arXiv:0910.1542.

In "week235" I mentioned an amazing paper by Baratin and Freidel called "Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams". They described a spin foam model that acts just like 4-dimensional flat Minkowski spacetime: couple it to interacting point particles, and you get the usual Feynman diagrams described in a new way!

The big news is that this spin foam model comes from the representations of a 2-group, instead of a group. Namely, the Poincaré 2-group. This is a 2-group I invented which has Lorentz transformations as objects and translations as endomorphisms of any object.

The Poincaré 2-group spin foam model was first studied by Crane, Sheppeard and Yetter. Baratin, Freidel, Wise and I spent a long time developing the theory of infinite-dimensional representations of 2-groups needed to make this model precise - see "week274" for more on all this. Now the details are falling into place, and a beautiful picture is emerging.

I should admit that the paper by Baratin and Wise deals with the Euclidean rather the Lorentzian version of this picture. I hope this is merely because the representation theory of the "Euclidean 2-group" is more tractable than that of the Poincaré 2-group. I hope everything generalizes to the Lorentzian case.

A lot to think about...

==endquote==

More at http://math.ucr.edu/home/baez/week281.html

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# Loop-String goodies in TWF 281 (that MTd2 spotted)

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