Meaning of low energy in loop quantum gravity

[Physics Monkey]

Meaning of "low energy" in loop quantum gravity

In the recent Immirzi parameter thread we accumulated some evidence that to resolve and/or clarify the issues raised there, it would be necessary to have an understanding of the flow to low energy or the flow from micro to macro in loopy models of gravity. This statement is almost trivial in field theory since we know very well now that low energy parameters and degrees of freedom need not be anything like those at high energy. However, it seems quite non-trivial in the context of loopy gravity.

What I have in mind is the question: what "energy" are we flowing to low values of in loopy gravity models? Perhaps energy is the wrong word in general, but it must eventually become the right word in some limits e.g. semiclassical gravity with weak quantum corrections around flat space. So I would like to discuss this issue, namely, what do we do know about generalized renormalization in loopy gravity models? How to define it, the difference between micro and macro, connection to semiclassical limit, universality, etc.

Also, I would just like to note that this problem is less severe or even absent for some models of emergent spacetime. Fotini's quantum graphity is one example where time is not emergent, energy is a sensible quantity, and we can meaningfully speak of the flow to low energy, although not perhaps the flow to long wavelengths in an unambiguous way.

It might also be interesting to discuss renormalization in other models of quantum gravity, for example, perturbative string theory or holographic duality. Indeed, within holographic duality, we have a good understanding of what renormalization in the dual field theory corresponds to in the bulk, but how should we think about renormalization in the bulk (or should we)?

 

[atyy]

There are two lines of work, and I don't know the connection between them.

In one of them, the semiclassical limit is supposed to be like perturbative quantum gravity on a background. To pick a background, people pick a boundray state that is has a suitable geometrical interpretation, and then propagate it into the bulk with spinfoams, hoping the resulting bulk will then be semiclassical http://arxiv.org/abs/0905.4082. The spinfoam formalism contains potentially divergent sums, and people talk about renormalization http://arxiv.org/abs/0810.1714 .

The second line follows, I think from Freidel and Livine's work in a 3D spinfoam/group field theory where they "integrated out" gravity and recovered non-commutative matter fields http://arxiv.org/abs/hep-th/0512113 . Apparently GFT has some similarity to non-commutative field theory, where UV/IR are also mixed. People, including Rivasseau, figured out how to renormalize some NCFTs. Now they are trying to renormalize GFT, with lots of nice speculation about phase transitions http://arxiv.org/abs/1103.1900 .

As usual, Markopoulou has an interesting paper from years ago which no one knows how to follow up. http://arxiv.org/abs/gr-qc/0203036

 

[marcus]

In the recent Immirzi parameter thread we accumulated some evidence that to resolve and/or clarify the issues raised there, it would be necessary to have an understanding of the flow to low energy or the flow from micro to macro in loopy models of gravity.

AFAIK, speaking of course as an outside observer (not as someone in the Loop community) the issue of renormalization is largely unexplored.

That is why it seems to me that Kowalski-Glikman Durka paper that appeared recently and punted to Ted Jacobson's 2007 paper is exciting and a little scary.

Jacobson pointed out that the issue was potentially important and has been largely ignored.
We can speculate but I find it hard to guess what will come out of this.

Atyy has several times suggested that Loop folks could turn to a "Group Field Theory" formulation, where renormalization has been already introduced. Rovelli has also mentioned GFT in this context. Personally I don't understand how that would work. GFT basically means that fields are defined on a group manifold---a cartesian product of copies of SU(2) or some other symmetry group---instead of on a simulacrum of spacetime. The fields in GFT are, so to speak, defined on the symmetries of the information, instead of on a picture of the world. Laurent Freidel at Perimeter is the one who named GFT, and has done important work in both areas (if they are in fact separate areas.)

Atyy may be able to say something meaningful about the GFT approach to Loop, with it's potential to include renormalization. Vincent Rivasseau in Paris, and Daniele Oriti at Potsdam are two prominent GFT people who have worked in LQG as well.

Oh, Rovelli has recently added someone to his group who has been doing GFT and Noncommutative Geometry, who was formerly working with Rivasseau, if I remember right.

I guess I could put it like this: the people are in place to make the move, if there is going to be one.
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Also the relative locality idea, that Freidel recently gave a talk about at the ILQGS (international LQG seminar), is interesting in the context. It is explicitly energy dependent and says, in effect, that spacetime itself "runs" with energy.
The observer's momentum space is curved, the inferred geometry of the world "runs" depending on the energy with which one probes it.

The Rel Loc conjecture is that each observer's momentum space or more correctly phase space is curved and that therefore distant observer's ideas of the universe (which events occur, which worldlines cross) cannot be entirely compatible. Extending out from one's local phase space one forms an idea of spacetime, but these ideas do not coincide in a single unique reality.

I had to mention this, because it is an idea which is, in a sense, antithetical to the conceptual basis of Loop Gravity, and Freidel (one of the most creative Loop people) has gotten interested in it----he is one of the authors of the initial paper on Rel Loc. (with Smolin and Kowalski-Glickman).

You could say that it is bad news for Loop for Freidel to get interested in Rel Loc. But I don't count those sorts of points. Basically creative turmoil at a serious fundamental level are good things and humanity gains in the long run.

That said, one could observe that Rel Loc is a philosophical nightmare. Physics does not happen in the world, it happens in an observer's phase space! Rel Loc is however testable. It is already proposed how to test for curvature in momentum space.
Perhaps, since it is falsifiable, it will simply go away like other nightmares do.

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That is all preamble/background. I will try to speculate as to how running Immirzi and or running G could be incorporated----to give a direct answer to your question. Hopefully others will have some definite ideas. It will take some time---just saw your thread---I'll get back to it.
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[EDIT] Great! I see Atyy already replied. That makes part of my post here unnecessary.

 

[atyy]

I had to mention this, because it is an idea which is, in a sense, antithetical to the conceptual basis of Loop Gravity, and Freidel (one of the most creative Loop people) has gotten interested in it----he is one of the authors of the initial paper on Rel Loc. (with Smolin and Kowalski-Glickman).

You could say that it is bad news for Loop for Freidel to get interested in Rel Loc. But I don't count those sorts of points. Basically creative turmoil at a serious fundamental level are good things and humanity gains in the long run.

No. The relationship is spin foams/GFT equivalence. In 3D and 4D gravity models you can get non-commutative fields, these have curved momentum space ( http://arxiv.org/abs/hep-th/0512113 , http://arxiv.org/abs/0903.3475 ). So he is still deeply interested in LQG.

The slightly different point of view he takes is that if GFT is fundamental, there is no need to restrict ourselves to GFTs that are so directly related to old LQG.

 

[marcus]

No. The relationship is spin foams/GFT equivalence. In 3D and 4D gravity models you can get non-commutative fields, these have curved momentum space ( http://arxiv.org/abs/hep-th/0512113 , http://arxiv.org/abs/0903.3475 ). So he is still deeply interested in LQG.

The slightly different point of view he takes is that if GFT is fundamental, there is no need to restrict ourselves to GFTs that are so directly related to old LQG.

Sorry, I don't understand. Oh! Maybe I see. You say that curved momentum space arises naturally in Loop Gravity. Yes, I'm familiar with that. It does, in fact, go back a long ways (at least to 2005).
So then you point out that (thanks in part to Sabine Hossenfelder's paper) curved momentum space MUST lead to Rel Loc.

So then you argue that, especially with the new Loop Gravity, which does not even have a spacetime manifold to confuse the issue by pretending to be a single unique world, Rel Loc is not "antagonistic" to Loop. It may even be compatible with it. And you suspect that Freidel is still deeply interested in Loop.

You say "take GFT as fundamental" and don't worry about the old canonical manifoldy LQG.
I actually think of Rovelli's new formulation in, say, http://arxiv.org/abs/1102.3660 , as Group-Fieldy already because the Hilbertspace is functions on a group manifold, but I think you mean something stronger.
What does it look like if you take GFT as fundamental?

 

[atyy]

I actually think of Rovelli's new formulation in, say, http://arxiv.org/abs/1102.3660 , as Group-Fieldy already because the Hilbertspace is functions on a group manifold, but I think you mean something stronger.
What does it look like if you take GFT as fundamental?

Yes, probably the new EPRL/FK models are already GFTs, since many spin foams can be translated into GFTs via http://arxiv.org/abs/gr-qc/0002095 . I think the formulation of EPRL/FK as GFT is done in http://arxiv.org/abs/1008.0354 . I was thinking more along the lines of AdS/CFT: if a theory without obvious gravity can have gravity, then GFTs are in that spirit, since GFTs don't have obvious gravity. But since AdS/CFT can be realized with more than one CFT, why not other GFTs too?

 

[Physics Monkey]

The flat space perturbative gravity renormalization story seems pretty sensible. Good to see that spinfoam type models can make some contact with that, but I guess that without a controlled way to study the semiclassical limit in loopy approaches it would be hard to get very precise about the renormalization group structure.

I have to say I don't have too favorable of an impression of non-commutative field theory. Based on what little I know about it, the issue of UV/IR mixing seems to call into question the whole basis of renormalization, at least the way I think about it. I wonder if there is a regulated model in which one can consider these issues?

 

[atyy]

Surprisingly, it is said that non-commutative field theories can be renormalized. I don't have even a handwavy picture of what is going on, but Rivasseau gives an overview here http://arxiv.org/abs/0705.0705 . Many of who worked on NCFT renormalization are now working on defining renormalization in group field theories http://arxiv.org/abs/1103.1900 .

From his review, the key insight came from a series of papers by Grosse and Wulkenhaar in 2003, with their conjectures tidied up in http://arxiv.org/abs/hep-th/0501036.

 

[atyy]

The Rivasseau review of NCFT remains impenetrable to me. Richard Szabo, assuming he's talking about the same thing, says more picturesquely "The proof is obtained by an exact mapping of the field theory onto a (infinite-dimensional) matrix model, which naturally arises due to the infinite degeneracy of Landau levels that provides a two index basis set of complete Landau wavefunctions for the expansion of the noncommutative fields. The duality-invariant cutoff is then naturally taken to be the matrix size N, and the wilsonian approach can be applied to the truncated model as N varies." http://arxiv.org/abs/0906.2913

And I would guess that has some relation to this 1/N expansion Gurau and Rivasseau are trying in group field theory http://arxiv.org/abs/1101.4182

 

[marcus]

...
And I would guess that has some relation to this 1/N expansion Gurau and Rivasseau are trying in group field theory http://arxiv.org/abs/1101.4182

Thanks for suggesting I include that in the "MIP" poll. I also added two more as write-ins (post #3 of the poll thread). Excellent papers* I somehow missed until just recently:

http://arxiv.org/abs/1102.5759
The complete 1/N expansion of colored tensor models in arbitrary dimension
Razvan Gurau
(Submitted on 28 Feb 2011)
"In this paper we generalize the results of [1,2] and derive the full 1/N expansion of colored tensor models in arbitrary dimensions. We detail the expansion for the independent identically distributed model and the topological Boulatov Ooguri model."

http://arxiv.org/abs/1103.1900
Towards Renormalizing Group Field Theory
Vincent Rivasseau
22 pages, 5 figures
(Submitted on 9 Mar 2011)
"We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the organizers of the Corfu 2010 Workshop on Noncommutative Field Theory and Gravity for encouraging us to write this review."

*also impenetrable in spots. :-)