What is group field theory, and its relation LQG, CDT?

[ensabah6]

What is group field theory, and its relation LQG, CDT? There's no wiki article on gft.

I am aware of the numerous articles on arix, could someone summarize what these articles mean?

 

[marcus]

for starters, in December of 2008 Oriti gave an intro level seminar talk at Perimeter on various approaches to (nonstring) QG
Here's a lead to the video and the PDF of his slides.
http://pirsa.org/08120040/
He had 26 slides for the whole talk and #17-21 were about GFT.

It is an interesting video for several reasons.
1. Oriti has assembled a book that just went on sale from Cambridge U. Press that covers all approaches to QG.
2. His own specialty is GFT.
3. The talk is recent. He has perspective. He knows GFT and it's connections with other approaches.

So the very brief part of that video is an intro to GFT and its relation to the rest.
The PIRSA format let's you go to any slide and start the talk from there, or at least it used to. I haven't used that feature lately. Otherwise you have to guess and drag the button.
If you don't like reading introductory papers on arxiv, then you may like watching video and hearing the spoken word. That may work better.

 

[ensabah6]

for starters, in December of 2008 Oriti gave an intro level seminar talk at Perimeter on various approaches to (nonstring) QG
Here's a lead to the video and the PDF of his slides.
http://pirsa.org/08120040/
He had 26 slides for the whole talk and #17-21 were about GFT.

It is an interesting video for several reasons.
1. Oriti has assembled a book that just went on sale from Cambridge U. Press that covers all approaches to QG.
2. His own specialty is GFT.
3. The talk is recent. He has perspective. He knows GFT and it's connections with other approaches.

So the very brief part of that video is an intro to GFT and its relation to the rest.
The PIRSA format let's you go to any slide and start the talk from there, or at least it used to. I haven't used that feature lately. Otherwise you have to guess and drag the button.
If you don't like reading introductory papers on arxiv, then you may like watching video and hearing the spoken word. That may work better.

Thanks Marcus I'll take a look at it --- it doesn't have a wiki artice as do lqg and cdt

 

[marcus]

Oriti gave another (longer) introductory talk on GFT at Perimeter in 2006.
I wouldn't recommend it because he doesn't use slides, he uses the chalk and blackboard method. He's younger and less experienced as a lecturer.
But you might want to take a look just for thoroughness.

It was part of Lee Smolin's Introduction to LQG series. He got Dan Oriti to come in as a guest lecturer a few times, and in lecture #21 he spends much of the hour on GFT.
At that point he was mostly talking about his hopes for GFT and explaining motivation.
He was especially motivated by what he saw as the potential connections with other approaches to QG. He presented GFT as able to unify and assume various shapes.

In fact you could say that GFT is a flexible calculation method with multiple applications. But I'm leery of putting my own spin on it. It is best if you go directly to a source like Oriti (one of the main proponents.)

I should say that what he saw in 2006 as potential has, to some extent, come about. For instance, now when they do calculations in covariant LQG---spinfoams---they often turn to GFT. It seems to be emerging as a viable way to accomplish stuff in various QG approaches.

Again, I am very reluctant to put my own limited interpretation (which will interfere with others' direct perception of source material) but to me GFT looks like an obvious thing to do once you have spin networks as the quantum state of geometry.

After all, an essential feature of a spin network (or the covariant spinfoam version) is the labels. And the labels refer to some chosen group. So why not take a generic network and look at the set of labels? Look at a cartesian product of many copies of the group and start working with that geometrically instead of working with the original spacetime continuum. Because the set of labels contains an idea of the quantum state of the geometry. So you can work with that instead of directly with spacetime.
And the deciding issue will be "is it more tractable? Does this make it easier to calculate?"
But don't quote me because what I've said is a gross oversimplification from a limited perspective. (I'm glossing over the distinction between group elements and group representations in order to communicate, in a handwavy manner, my intuition about what is going on.

Oriti gave 3 consecutive introductory talks in Smolin's 2006 series. The third one was about GFT. I think this is the right link:
http://pirsa.org/06030029
Again, it does not have slides etc etc. The brief part of his 2008 talk I linked to earlier is probably a better introduction, but I include this just in case.

 

[marcus]

Another GFT paper by Oriti came out today:

http://arxiv.org/abs/0903.3970
Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
Daniele Oriti
13 pages; contribution to the proceedings of the D.I.C.E. 2008 workshop
(Submitted on 23 Mar 2009)
"We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field theories for matter directly from the GFT action, in both 3 and 4 dimensions and in both Riemannian and Lorentzian signatures. As such they represent an important step, we argue, in bridging the gap between a quantum, discrete picture of a pre-geometric spacetime and the effective continuum geometric physics of gravity and matter, using ideas and tools from field theory and condensed matter analog gravity models, applied directly at the GFT level."

 

[ensabah6]

Thanks Marcus,

I did see one of Oriti's papers where he talks about condense matter analogues, is this related to Wen's string nets and Alexander's loop gravity as a quantum fluid?

 

[marcus]

I guess everybody saw the paper that came out two days ago (I posted it on the biblio thread 22 March)

http://arxiv.org/abs/0903.3475
4d Deformed Special Relativity from Group Field Theories
Florian Girelli, Etera R. Livine, Daniele Oriti
23 pages
(Submitted on 20 Mar 2009)
"We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF-theory in 4 space-time dimensions. This is done at a non-perturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the non-commutative field theory governs their effective dynamics."

GFT has "connections" with a lot of things, especially LQG, spinfoams, BF theory, CDT.

So now we have contact brewing with DSR and with matter fields.

It probably connects with a lot of more speculative ideas that are appealing to think about but that you can't calculate much with. I can't spell out the connections with the more nebulous approaches. They may not be what is interesting anyway. What I see happening is that people in LQG use GFT to calculate with. It seems good for that. Powerful pragmatic framework. Flexible in applications. Maybe someone else will have a different perspective on it.

 

[ensabah6]

I guess everybody saw the paper that came out two days ago (I posted it on the biblio thread 22 March)

http://arxiv.org/abs/0903.3475
4d Deformed Special Relativity from Group Field Theories
Florian Girelli, Etera R. Livine, Daniele Oriti
23 pages
(Submitted on 20 Mar 2009)
"We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF-theory in 4 space-time dimensions. This is done at a non-perturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the non-commutative field theory governs their effective dynamics."

GFT has "connections" with a lot of things, especially LQG, spinfoams, BF theory, CDT.

So now we have contact brewing with DSR and with matter fields.

It probably connects with a lot of more speculative ideas that are appealing to think about but that you can't calculate much with. I can't spell out the connections with the more nebulous approaches. They may not be what is interesting anyway. What I see happening is that people in LQG use GFT to calculate with. It seems good for that. Powerful pragmatic framework. Flexible in applications. Maybe someone else will have a different perspective on it.

I was thinking of below -- Is Oriti stating that LQG spacetime gives rise to emergent gravity and matter much in the manner as Volvovik's helium-3 superfluid?

http://arxiv.org/abs/0903.3970
Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
Daniele Oriti
13 pages; contribution to the proceedings of the D.I.C.E. 2008 workshop
(Submitted on 23 Mar 2009)
"We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field theories for matter directly from the GFT action, in both 3 and 4 dimensions and in both Riemannian and Lorentzian signatures. As such they represent an important step, we argue, in bridging the gap between a quantum, discrete picture of a pre-geometric spacetime and the effective continuum geometric physics of gravity and matter, using ideas and tools from field theory and condensed matter analog gravity models, applied directly at the GFT level."