EPRL/FK Group Field Theory (Vincent Rivasseau, Razvan Gurau, Joseph Ben Geloun)

[marcus]

MTd2 spotted this one. It was time for a paper like this. Very glad to see it.

http://arxiv.org/abs/1008.0354

 

[atyy]

I'm glad to see this!

Thanks God for string theory - no? :tongue:

 

[marcus]

Thank God for modern mathematics in general.

Rivasseau's main focus seems to be QFT---noncommutative lately. Seems to have breadth and poise (no bias as to what means to use). Is that your impression?
http://arxiv.org/find/grp_physics/1/au:+Rivasseau/0/1/0/all/0
I would guess Rivasseau has command of a wide range of string tools as well.

 

[marcus]

In case someone is just joining us, EPRL/FK is the form of Loop Quantum Gravity which appeared starting around 2008.

EPRL is what Rovelli calls "new LQG" and FK is a close cousin.
The initials stand for Engle Pereira Rovelli Livine Freidel Krasnov.

For the past couple of years I have been seeing Gurau in the seminar video from Perimeter. But there is only one video seminar talk by him that I know of:
http://pirsa.ca/08050027/
Renormalization in Noncommutative Quantum Field Theory
This can give an idea of who he is and what his interests are.

I think most of us are already somewhat familiar with Rivasseau, but here is a video talk by him in case anyone is curious.
http://pirsa.ca/08110023/
Renormalization, an overview
"We review how renormalization, born in quantum field theory has evolved into a rather universal tool to analyze the change of physical laws under scaling. Recent developments in non commutative geometry with hopefully potential applications to the quantization of gravity will be discussed."

The one talk by Geloun I could find happened to be about Group Field Theory.
http://pirsa.ca/09120029/
Colored group field theory: Scaling properties and positivity
"The scaling analysis in the large spin limit of Feynman amplitudes for the Bosonic colored group field theory are considered in any dimension starting with dimension 4. By an explicit integration of two colors, we show that the model is positive. This formulation could be useful for the constructive analysis of this type of models."
(I had not seen a Geloun talk before--I got a good impression. Only time to watch the first 15 or 16 minutes.)

 

[atyy]

Rivasseau's main focus seems to be QFT---noncommutative lately. Seems to have breadth and poise (no bias as to what means to use). Is that your impression?
http://arxiv.org/find/grp_physics/1/au:+Rivasseau/0/1/0/all/0
I would guess Rivasseau has command of a wide range of string tools as well.

Yes - because renormalization of noncommutative field theories started in string theory. Originally noncommutative phi^4 was thought nonrenormalizable because of UV/IR mixing http://arxiv.org/abs/hep-th/9912072. However, they were found to be renormalizable http://arxiv.org/abs/hep-th/0307017, and in fact asymptotically safe http://arxiv.org/abs/hep-th/0612251! As you know, group field theory and noncommutative field theory are linked, which is why Ben Goulon, Gurau,Rivasseau,Magnen,Tanasa etc who worked on NCFT renormalization are now interested in GFT.

 

[atyy]

I think most of us are already somewhat familiar with Rivasseau, but here is a video talk by him in case anyone is curious.
http://pirsa.ca/08110023/
Renormalization, an overview
"We review how renormalization, born in quantum field theory has evolved into a rather universal tool to analyze the change of physical laws under scaling. Recent developments in non commutative geometry with hopefully potential applications to the quantization of gravity will be discussed."

Nov 5, 2008

"Today is a special historic day so I cannot resist:

Cheers Obama!

Now let's renormalize the world together!"

Wow, he made a testable prediction 2 years back! Much better than string theory!

 

[MTd2]

Originally noncommutative phi^4 was thought nonrenormalizable because of UV/IR mixing http://arxiv.org/abs/hep-th/9912072.

I didnt find in the paper where it was stated it was non renormalizable. It seems that they wrote that due UV/IR mixing the theory looks stringy for high momentum. It is vague, but given that string theory is renormalizable, I think the authors would say at that time that this theory would be more likely to be renormalizable than not.

 

[atyy]

I didnt find in the paper where it was stated it was non renormalizable. It seems that they wrote that due UV/IR mixing the theory looks stringy for high momentum. It is vague, but given that string theory is renormalizable, I think the authors would say at that time that this theory would be more likely to be renormalizable than not.

Yes, I think they said something more like they didn't know how to renormalize it. I guess the difficulties they pointed out are in (3.11), (3.12) and the discussion following (3.20).

 

[marcus]

I think we are going to be following this EPRL/FK Group Field Theory development some. I will get the abstract of the earlier paper that they refer to a lot in this one. Their reference [9].

Also we should note where their terminology differs slightly from Rovelli's "marseille" vocabulary. Rovelli says a spinfoam is made of vertices edges and faces.
Rivasseau's team says:
vertices
stranded lines (also called 'propagators')
faces (= closed circuit of strand)

It is very simple. In a 4D world, for example, all the edges are like 4-lane highways.
And you don't have to draw in the faces because a face is defined by the fact that one of the lanes splits off at a vertex and loops around it. The faces are just the places where a strand loops around and makes a circuit.

It is just a different notation for essentially the same spinfoam idea. What they call "stranded lines" are what I am imagining as 4-lane highways. There are some pictures here, on pages 3 and 4 and following:

http://arxiv.org/abs/1007.3150
Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
Thomas Krajewski, Jacques Magnen, Vincent Rivasseau, Adrian Tanasa, Patrizia Vitale
35 pages, 5 figures
(Submitted on 19 Jul 2010)
"We investigate the group field theory formulation of the EPRL/FK spin foam models. These models aim at a dynamical, i.e. non-topological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory amplitudes and compare it with existing results, in particular for a second order correction to the EPRL/FK propagator."

This LQG spinfoam GFT initiative from Rivasseau's group (Paris, Orsay) is a fairly new development. As far as I know that July 2010 paper was the first. And this one, that prompted starting this thread, is the second:

http://arxiv.org/abs/1008.0354
EPRL/FK Group Field Theory
Joseph Ben Geloun, Razvan Gurau, Vincent Rivasseau
20 pages, 2 figures
(Submitted on 2 Aug 2010)
"The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model."