Baratin and Freidel: a spin foam model of ordinary particle physics

[marcus]

Baez started the thread by talking about this paper, which has just come out (and maybe the follow-up paper which he may be co-authoring with B and F)

He called the thread
Baratin and Freidel: a spin foam model of ordinary particle physics

Now that the paper is out, perhaps we should ask some questions like

What does the paper do that we expected?
Does it do anything that was not anticipated in our (or JB's) discussion?
Does it leave anything out, that we expected----maybe putting it off to a later paper?

Is this really a (background independent) model of ordinary particle physics?[/color]

If it is, that is a first----ordinary particle physics is built on rigid pre-ordained normally flat background geometry----but the spinfoam approach is manifestly a background independent formulation. It does not appeal at any point to a set-up geometry.

It looks like Freidel COAXED A SENSE OF AMBIENT GEOMETRY INTO THE FEYNMAN DIAGRAM ITSELF. So that the Feynman diagram knows enough about the geometry that it doesn't have to have it spelled out ahead of time. And it has a ZERO-GRAVITY LIMIT where you let the Newton parameter G_N go to zero, so space flattens out, and you get the same amplitudes as you would in usual QFT on flat spacetime.

What seems to be missing, for me, in the paper is a confirmation that the spinfoam model has deformed Poincare symmetry. In the earlier "Hidden" paper, where B and F dealt with the 3D case, there was the expectation of an energy-dependent speed of light----something that GLAST could test.
I don't see that here. So I am asking anyone else who has been reading the paper what they think.
==============

for reference, here is the new paper:
http://arxiv.org/abs/hep-th/0611042
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
Aristide Baratin, Laurent Freidel
28 pages, 7 figures

"We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the symmetries of this Feynman graph spin foam model and give the gauge-fixing prescriptions. We also show that the gauge-fixed partition function is invariant under Pachner moves of the triangulation, and thus defines an invariant of four-dimensional manifolds. Finally, we investigate the algebraic structure of the model, and discuss its relation with a quantization of 4d gravity in the limit where the Newton constant goes to zero."

Here is the promised follow-up, their reference [23], expected to be co-authored with JB
[23] J. Baez, A. Baratin, L. Freidel, On the representation theory of the Poincaré 2-group, To appear.

Here is the earlier "Hidden" paper by B and F, dealing with the 3D case
http://arxiv.org/abs/gr-qc/0604016
Hidden Quantum Gravity in 3d Feynman diagrams
Aristide Baratin, Laurent Freidel
35 pages, 4 figures

"In this work we show that 3d Feynman amplitudes of standard QFT in flat and homogeneous space can be naturally expressed as expectation values of a specific topological spin foam model. The main interest of the paper is to set up a framework which gives a background independent perspective on usual field theories and can also be applied in higher dimensions. We also show that this Feynman graph spin foam model, which encodes the geometry of flat space-time, can be purely expressed in terms of algebraic data associated with the Poincaré group. This spin foam model turns out to be the spin foam quantization of a BF theory based on the Poincaré group, and as such is related to a quantization of 3d gravity in the limit where the Newton constant G_N goes to 0. We investigate the 4d case in a companion paper where the strategy proposed here leads to similar results."

I may be mistaken---maybe I should not have been expecting news about an energy-dependent speed of light. I don't see any mention of that in the abstract, have to check.

 

[marcus]

...
Here is the promised follow-up, their reference [23], expected to be co-authored with JB

[23] J. Baez, A. Baratin, L. Freidel, On the representation theory of the Poincaré 2-group, To appear.

...

In his most recent, This Week's Finds #269, John Baez remarks that he is hard at work with Baratin, Freidel, and Wise on a paper on representations of 2-groups.

It's as if there has been a hiatus of about two years! 2006 to 2008. Good luck to them! Maybe some of the stuff in this thread will provide a useful review and warmup for anyone who wants to get prepared to understand the 2-group paper they are working on, when it is ready. In the brief mention in TWF #269 the word "gnarly" is used, so be forewarned.

 

[MTd2]

In his most recent, This Week's Finds #269, John Baez remarks that he is hard at work with Baratin, Freidel, and Wise on a paper on representations of 2-groups.

It's as if there has been a hiatus of about two years! 2006 to 2008. Good luck to them!

You know that doesn't mean he is back to research on LQG neiter Spin Foam stuff.

 

[marcus]

Certainly MTd2! You make an obvious point. The representation of 2-groups is a math research topic of general interest. It is not an applied research topic and the interest is obviously not limited to Quantum Gravity. Let me say things a little more clearly, to make sure you do not misunderstand me:
In 2006, Baez, Baratin and Freidel had a paper in preparation on the representation of 2-groups. This paper did not appear. There was a hiatus. Now it seems that they are again working on the representation of 2-groups---and Derek Wise has joined them making a fourth author.

You, in effect, raise the issue of what relation exists between the general math problem of 2-groups on the one hand, and quantum gravity on the other. That's a very interesting question that is talked a bit about in this thread. I think I understand the relation a little, though not completely. This thread is, in a sense, about the quantum gravity motivation for exploring 2-groups.

One way to understand the QG motivation, if you don't want to read the beginning of the thread, where JB explains it, is to look at the research history of the people. The research interests of Freidel, Baratin, and Wise are primarily in QG----Freidel especially in spinfoams.
In 2005 Freidel (with Livine and others) got a very interesting result including matter in spinfoam at 3D. Roughly speaking he found that in 3D the spinfoams of gravity and the Feynman diagrams of matter are, at a basic level, the same entity. A spinfoam is a combinatorial structure colored with group representations. Baratin was a postdoc working with Freidel part of that time.

The problem, which Freidel, Baratin, and others faced at that time was how to extend the results to 4D. One idea of how to do this involved coloring not only with group representations but with 2-group representations.

But there is basic mathematical ground-work to be done on 2-group representation theory before that application can be tackled. One probably needs to be able to classify the representations of the Poincaré 2-group. At least. In order to make it work. Not being an expert, I cannot tell, but I think that as the solution of an important pure math problem this would be noteworthy----in part because of the quantum gravity motivation but also for general aesthetic reasons. However the problem may not be tractable! It may be hellishly difficult!

Back in 2005 Derek Wise, another QG researcher, was doing his PhD thesis with John Baez, working on a different quantum gravity problem (not spinfoam) but one which I think could also use 2-groups. His thesis-related work (2007) is interesting, you might enjoy looking it up. Now postdoc at UC Davis with Steve Carlip.

So now we have a hint (just a brief mention) that JB might be working (he used the words "hard" and "gnarly") with these 3 quantum gravitists on a basic mathematical problem with strong QG motivation. What will come of this? Will they succeed? Will the work reach a satsifactory conclusion? Whatever they are working on seems to be tough, because the paper cited as in prep, back in 2006, never appeared. However Laurent Freidel is very stubborn. (I have watched his research since 2003 and can tell at least that much about him.) As bystanders, you and I are allowed to make bets, MTd2. I will bet that this time the paper will take shape to the authors' satisfaction, and we will see it in the next 6-12 months. Possibly earlier. So now would be the time to refresh one's ideas about 2-groups and about Freidel's way of uniting spinfoams with Feynman diagrams and establishing ordinary QFT in the spinfoam context.

 

[MTd2]

uniting spinfoams with Feynman diagrams and establishing ordinary QFT in the spinfoam context.

So that, you could also study supergravity from the point of view of spianfoams?

"A spinfoam is a combinatorial structure colored with group representations."

I recall reading the names "colored" and "diagrams" close to each other, in a method to help calculate the away divergencies in supergravities N=8, in one of those articles from Carrasco. I don't understand much, and I know it is not related at all to spinfoams. But what you said rhymes with that.

 

[marcus]

So that, you could also study supergravity from the point of view of spinfoams?
...

I don't have a lot of useful information about this. Supergravity has already been studied in the LQG context. I don't happen to have the links but there are papers and I guess any of us could dig them up with a keyword search. As a general framework LQG is compatible with both SUGRA and with extra dimensions. So presumably spinfoam would be equally.

But as far as I know, those papers go way back. At some point, probably in the 1990s or anyway before 2003, somebody checked to make sure LQG could accommodate SUGRA and D>4. But I don't know of any recent interest in that.

Here is a possible suggestion, where you might find something: check out the September 2008 Sussex workshop. I'll get a link. It includes top leaders in quantum gravity research like John Barrett, Renate Loll, and Laurent Freidel. Since N=8 SUGRA has been in the news a lot, if it holds any promise for non-perturbative QG then I would guess it would come up in the Sussex workshop. I've seen signs that N=8 supergravity is on the agenda, so let's keep an eye out for it.

If anything good can come out of cross-fertilization between different lines of nonperturbative field theory research, this Sussex workshop is going to exemplify it and set a pattern for the future. So check out the schedule (I expect you already have, actually!) Here's a post of mine with links:

the next major workshop/conference that I know about, is the one in Sussex 17-19 September
I posted an announcement about this in the ANNOUNCEMENTS thread back in June, month before last.
What I want to do here is study the topics, focus, and lineup of speakers for clues about where the field is going
Continuum and Lattice Approaches to Quantum Gravity
http://www.ippp.dur.ac.uk/Workshops/08/CLAQG
Among other things it will feature talks by
* Jan Ambjorn (NBI Copenhagen)
* John Barrett (U Nottingham)
* Laurent Freidel (ENS Lyon and Perimeter Institute)
* Renate Loll (U Utrecht)
* Max Niedermaier (U Tours)
* Roberto Percacci (SISSA Trieste)
* Martin Reuter (U Mainz)
* Thomas Thiemann (AEI Golm and Perimeter Institute)

You can see the emphasis
Triangulations----Ambjorn, Loll
Asymptotic Safety----Reuter, Percacci, Niedermeyer,
Spinfoam---Freidel, Barrett
canonical LQG---Thiemann

The three days of talks will be preceded by a school 15-16 September, to provide extra preparation for participants who wish it
Non-perturbative Methods in Quantum Field Theory
http://www.ippp.dur.ac.uk/Workshops/08/NPMQFT
Some of the lectures will be as follows:

* Basics of the non-perturbative renormalisation group (D. Litim, U Sussex)
* Basics of the Renormalization Group for QCD and confinement (J.M. Pawlowski, U Heidelberg)
* Basics of QCD on the lattice (O. Philipsen, U Muenster)
* Basics of asymptotic safety for gravity (M. Niedermaier, U Tours)
* Basics of the Renormalization Group for quantum gravity (M. Reuter, U Mainz)
* Basics of lattice quantum gravity I (R. Loll, U Utrecht)
* Basics of lattice quantum gravity II (J. Barrett, U Nottingham)

...

Here is the program:
http://www.ippp.dur.ac.uk/Workshops/08/CLAQG/Programme/

I see that Bjerrum-Bohr, from Princeton, is on the program. Let me see what his line of research is.

 

[marcus]

Ahah! I thought I remembered that Bjerrum-Bohr was into N=8 SUGRA!

So that too is part of the Sussex workshop. Look at Bjerrum-Bohr's recent papers:

1. arXiv:0806.1726 [ps, pdf, other]
Title: On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
Authors: N. E. J. Bjerrum-Bohr, Pierre Vanhove
Comments: Latex. 12 pages, 1 figure. Contribution to the proceedings of the 3rd meeting of the RTN `` Constituents, Fundamental Forces and Symmetries of the Universe'' in Valencia (Spain) and Quarks 2008 at Sergiev Posad (Russia). v2: minor corrections
Subjects: High Energy Physics - Theory (hep-th)
2. arXiv:0805.3682 [ps, pdf, other]
Title: Absence of Triangles in Maximal Supergravity Amplitudes
Authors: N. E. J. Bjerrum-Bohr, Pierre Vanhove
Comments: 16 pages, RevTeX4 format
Subjects: High Energy Physics - Theory (hep-th)
3. arXiv:0802.0868 [ps, pdf, other]
Title: Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
Authors: N. E. J. Bjerrum-Bohr, Pierre Vanhove
Comments: 25 pages. 2 eps pictures, harvmac format. v2: version to appear in JHEP. Equations (3.9), (3.12) and minor typos corrected
Subjects: High Energy Physics - Theory (hep-th)
4. arXiv:0709.2086 [ps, pdf, other]
Title: Analytic Structure of Three-Mass Triangle Coefficients
Authors: N. E. J. Bjerrum-Bohr, David C. Dunbar, Warren B. Perkins
Comments: 22 pages; v3: NMHV n=point expression added. 7 point expression removed
Subjects: High Energy Physics - Phenomenology (hep-ph)
5. arXiv:gr-qc/0610096 [ps, pdf, other]
Title: On the parameterization dependence of the energy momentum tensor and the metric
Authors: N. E. J. Bjerrum-Bohr, John F. Donoghue, Barry R. Holstein
Comments: 8 pages, 2 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)
6. arXiv:hep-th/0610043 [ps, pdf, other]
Title: The No-Triangle Hypothesis for N=8 Supergravity
Authors: N. E. J. Bjerrum-Bohr, David C. Dunbar, Harald Ita, Warren B. Perkins, Kasper Risager
Comments: 43pages
Journal-ref: JHEP 0612 (2006) 072
Subjects: High Energy Physics - Theory (hep-th)

 

[MTd2]

Marcus, I guess this is very pertinent:

"Strings, quantum gravity and non-commutative geometry on the lattice
Authors: J. Ambjorn
(Submitted on 9 Jan 2002)

Abstract: I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods."

http://arxiv.org/PS_cache/hep-lat/pdf/0201/0201012v1.pdf

 

[marcus]

I think what we need to do, to keep this thread on topic, is to see how things relate what what Baez calls higher gauge theory---or with 2-groups.
The most basic way to look at the topic is it has to do with labeling spinfoams with reps of 2-groups instead of ordinary groups.
And doing gauge theory with 2-groups instead of ordinary groups, which I guess for brevity sake you could call 1-groups.

As I see it, it is still undecided whether quantum gravity NEEDS 2-groups. Maybe they are the key to success, maybe not. In any case they represent potentially powerful new mathematics and they will be developed (by people with good mathematical instincts) and they will be useful for something----maybe understanding space and matter fields, maybe something else.

I don't want to spend all my time thinking about 2-groups, but on the other hand I want to stay alert and interested in case any news comes up. that is the reason for keeping tabs on this thread.

 

[MTd2]

I think what we need to do, to keep this thread on topic

So, why you posted about a conference on "Continuum and Lattice Approaches to Quantum Gravity"?

 

[marcus]

Look back at your post #125, MTd2
I posted about that conference because I was trying to respond to this post of yours, which was off topic.

So that, you could also study supergravity from the point of view of spianfoams?

"A spinfoam is a combinatorial structure colored with group representations."

I recall reading the names "colored" and "diagrams" close to each other, in a method to help calculate the away divergencies in supergravities N=8, ...

I realized later I should not have tried to respond to a question about supergravity, because it is unrelated to the thread. But at that time I wanted to try to respond, so I mentioned this conference that is a kind of bridge. It brings a N=8 SUGRA expert together with Spinfoam experts like Laurent Freidel and John Barrett.

It didn't help to answer about something off topic, did it?

 

[MTd2]

It didn't help to answer about something off topic, did it?

It did :) . But I think you answer is on topic if posted on this thread, so... I will repost my post #128 there :)

 

[marcus]

With any luck, sometime soon you can read this paper on the arXiv:

Aristide Baratin and Laurent Freidel
Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams

The idea is that any ordinary quantum field theory in 4d Minkowski spacetime can be reformulated as a spin foam model. This spin foam model is thus a candidate for the G -> 0 limit of any spin foam model of quantum gravity and matter!

In other words, we now have a precise target to shoot at. We don't know a spin foam model that gives gravity in 4 dimensions, but now we know one that gives the G -> 0 limit of gravity: i.e., ordinary quantum field theory. So, we should make up a spin foam model that reduces to Baratin and Freidel's when G -> 0.

The fascinating thing I noticed is that their spin foam model seems to be based on the Poincare 2-group. I invented this 2-group in my http://www.arxiv.org/abs/hep-th/0206130" . The physical meaning of their spin foam model was unclear, and some details were not worked out, but it was very tantalizing. What did it mean?

I now conjecture - and so do Baratin and Freidel - that when everything is properly worked out, Crane and Sheppeard's spin foam model is the same as Baratin and Freidel's. So, it gives ordinary particle physics in Minkowski spacetime, at least after matter is included (which Baratin and Freidel explain how to do).

If this is true, one can't help but dream...

... that deforming the Poincare 2-group into some sort of "quantum 2-group" could give a more interesting spin foam model: ideally, something that describes 4d quantum gravity coupled to matter! This more interesting spin foam model should reduce to Baratin and Freidel's in the limit G -> 0.

Of course this dream sounds "too good to be true", but there are some hints that it might work, to be found in http://arxiv.org/abs/hep-th/0501191" . In particular, they describe gravity in way (equation 26) which reduces to BF theory as G -> 0.

Optimistic hopes in quantum gravity are usually dashed, but stay tuned.

This is the initial post of this thread. What it talks about is stuff that didn't really take shape until just now. Baez has posted a 2-groups paper he did with Laurent Freidel, Aristide Baratin, and Derek Wise.

http://math.ucr.edu/home/baez/2rep.pdf
Infinite-Dimensional Representations of 2-Groups
John Baez, Aristide Baratin, Laurent Freidel, Derek K. Wise

AFAIK this paper was posted 23 December 2008. But it is somehow a continuation of what Baez said at the beginning of this thread, in June 2006

 

[MTd2]

Marcus, in that article, a applications in spim foams are proposed as possible aplications:

"We conclude with some possible avenues for future investigation. First, it will be interesting to study examples of the general theory described here. Representations of the Poincare 2-group have already been studied by Crane and Sheppeard [14], in view of obtaining a 4-dimensional state sum model with possible relations to quantum gravity. Representations of the Euclidean 2-group (with G = SO(4) acting on H = R4 in the usual way) are somewhat more tractable. Copying the ideas of Crane and Sheppeard, this 2-group gives a state sum model [7, 8] with interesting relations to the more familiar Ooguri model."

[7] A. Baratin and L. Freidel, Hidden quantum gravity in 4d Feynman diagrams, Class. Quant. Grav. 24 (2007), 2027-2060. Also available as http://arXiv.org/pdf/hep-th/0611042.

[8] A. Baratin and L. Freidel, State-sum dynamics of at space, in preparation.

[14] L. Crane and M. D. Sheppeard, 2-Categorical Poincare representations and state sum applications,
available as arXiv:math/0306440.

There are other references that shows that shows this approach will soon find concreteapplication.