# Existence of pure quantum gravity

#### atyy

Is pure quantum gravity known to exist?

I had thought it exists in 3D, but Strominger writes http://arxiv.org/abs/0906.1313 "Determining Z for pure 3D quantum Einstein gravity - if it exists - is an important open problem"

Eg. Does the Turaev-Viro model not describe 3D QG?

Related Beyond the Standard Model News on Phys.org

#### marcus

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I'd like to hear your summary, if you have looked those sources over and have some general impressions.

It is striking how much work still is being devoted to 3D pure QG.
As I recall (odd bit of trivia) 3D QG was the topic of Witten's talk at the Strings 2007 conference in Madrid. At the end, someone from the audience asked him what the connetion was with the string program and he told them (I don't remember exactly what it was.)

That same week Loops 2007 was going on at Morelia in Mexico and Rovelli gave a kind of "where do we go from here" roadmap talk at the end, where he mentioned that since so much had been done on 3D he would urge people not to work on it unless they had some really good reason in mind--some direct bearing on the harder problem of 4D. It impressed me because he was actually telling the young researchers there to "work on the hard problem! Don't keep doodling around with 3D just because it is easier to get publishable results."

Every effort to lead involves risk. You only know later how it turns out. It may be that there is some essential insight still to be gotten from 3D QG! Perhaps Strominger will surprise us with some valuable discovery there. Or maybe not. I'd be glad to hear what you envision as possibilities.

Then the more interesting question: what do you conclude about 4D QG? Does a theory exist? What state does it seem to be in? Are you thinking of some perturbative approach? I mean where you have a series including the terms allowed by symmetry. Or some TQFT approach where you start with a BF formulation?

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#### atyy

Criteria:

1) It should be a consistent quantum theory
2) It should have the right semiclassical/classical limit

and maybe

3) It should have the BTZ black hole and give us its entropy

#### Sardano

Criteria:

1) It should be a consistent quantum theory
2) It should have the right semiclassical/classical limit

and maybe

3) It should have the BTZ black hole and give us its entropy

Several months ago, I attended some Enrique Alvarez lectures on Quantum Gravity, and the first thing he did was to show us that it was not possible to obtain a Quantum Gravity theory ignoring all the others interaction. That you should take all of them into account in order to have a well defined Quantum Gravity theory, which would be an unified theory of the four known interactions.

In light of this comments, some guy asked that then LQG should be wrong!... Enrique Alvarez with all due respect said that he thinks LQG is not correct but that all the possibilites should be investigated... there was big laughs on the audience.

The argument was based on QFT, the theories that are being experimentally cheked in accelerators all over the world in hundred of ways (GR has only a few experimental tests). I will look for the reference of this lectures and I will post it, in case someone is interested.

#### atyy

Several months ago, I attended some Enrique Alvarez lectures on Quantum Gravity, and the first thing he did was to show us that it was not possible to obtain a Quantum Gravity theory ignoring all the others interaction. That you should take all of them into account in order to have a well defined Quantum Gravity theory, which would be an unified theory of the four known interactions.
How about the 3D case? Strominger's http://arxiv.org/abs/0906.1313 (fourth problem) indicate that he's unsure, particularly in the AdS case, where there's the BTZ black hole.

I had long thought the 3D case was covered by Witten's Chern-Simons theory, or by the Turaev-Viro theory. But Strominger refers to Witten's http://arxiv.org/abs/0706.3359 which casts doubt on the former, and I'm not sure Turaev-Viro is known to give the right semiclassical limit.

I will look for the reference of this lectures and I will post it, in case someone is interested.
That's be cool if you can find it, thanks.

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#### Finbar

Several months ago, I attended some Enrique Alvarez lectures on Quantum Gravity, and the first thing he did was to show us that it was not possible to obtain a Quantum Gravity theory ignoring all the others interaction. That you should take all of them into account in order to have a well defined Quantum Gravity theory, which would be an unified theory of the four known interactions.
What he say's here http://arxiv.org/pdf/1011.0543 is

"Then all couplings in the effective Lagrangian become of order unity, and there is no decoupling limit in which gravitation can be considered by itself in isolation from all other interactions. This then seems the minimum prize one has to pay for being interested in quantum gravity; all couplings in the derivative expansion become important simultaneously. No significant differences appear when supergravity is considered.
In conclusion, it does not seem likely that much progress can be made by some- how quantizing Einstein-Hilbert’s Lagrangian in isolation. To study quantum gravity means to study all other interactions as well."

But these interactions can still be purely gravitational ones. He is not saying that we have to couple the theory to matter to get a consistent theory just that we shouldn't only consider the EH Lagrangian.

So i think maybe you misunderstood him? We don't need a unify QG with the other forces to get a consistent theory.

#### fzero

Homework Helper
Gold Member
But these interactions can still be purely gravitational ones. He is not saying that we have to couple the theory to matter to get a consistent theory just that we shouldn't only consider the EH Lagrangian.

So i think maybe you misunderstood him? We don't need a unify QG with the other forces to get a consistent theory.
No, what he's saying is that if there is matter and nongravitational interactions at scales $$E \ll M_P$$, then at $$E \sim M_P$$ these interactions remain and, furthermore, their couplings are of order unity. There is therefore no regime where pure gravity exists in the presence of other interactions. There are further arguments in http://arxiv.org/abs/hep-th/0601001 that gravity is always the weakest force in such a scenario.

This is an important concept when we ask about how to quantize gravity in a real-world scenario. Whether or not there are quantum theories of pure gravity as toy models remains an interesting question, but perhaps not one that is completely relevant to describing our universe.

#### atyy

So I guess the situation is

-Turaev-Viro model describes 3D Riemannian gravity with positive cosmological constant
http://arxiv.org/abs/gr-qc/9905087
http://arxiv.org/abs/gr-qc/0311066

-However with positive cosmological constant, there are no known observables for someone inside the universe, so Witten examines the case of negative cosmological constant.
-Witten's Chern-Simons proposal for 3D (Lorentzian?) gravity with negative cosmological constant is probably wrong.
-So he makes a new proposal for pure 3D AdS quantum gravity to be described by 2D boundary CFT
http://arxiv.org/abs/0706.3359
http://math.ucr.edu/home/baez/week254.html

#### atyy

So I guess the situation is

-Turaev-Viro model describes 3D Riemannian gravity with positive cosmological constant
http://arxiv.org/abs/gr-qc/9905087
http://arxiv.org/abs/gr-qc/0311066

-However with positive cosmological constant, there are no known observables for someone inside the universe, so Witten examines the case of negative cosmological constant.
-Witten's Chern-Simons proposal for 3D (Lorentzian?) gravity with negative cosmological constant is probably wrong.
-So he makes a new proposal for pure 3D AdS quantum gravity to be described by 2D boundary CFT
http://arxiv.org/abs/0706.3359
http://math.ucr.edu/home/baez/week254.html
Actually, I'm not so sure about the Turaev-Viro model and 3D gravity. Here are a few more papers with interesting discussions of the relationship.

http://arxiv.org/abs/hep-th/9110057
"Therefore it would be better to consider the Regge action appeared in our model as the CS action, rather than the Einstein action. The strange i factor may indicate the subtlety in the correspondence between the Euclidean gravity and a CS theory."

http://arxiv.org/abs/hep-th/9804185v1
"Thus, if there indeed exist a phase of the quantum BF theory in which non-degenerate E fields dominate, then one can gain some control over the spacetime volume in (2+1) quantum gravity using the results from BF theory. If, on the other hand, the path integral of BF theory is always dominated by highly degenerate solutions, as may well be the case, then the two theories have very little to do with each other, and the spacetime volume of BF theory is not the same as the volume in gravity. At the present stage of our understanding of quantum gravity it is hard to tell which of this two possibilities is realized."

http://arxiv.org/abs/1012.4784
"In three dimensions, the Turaev-Viro invariant is related to Euclidean gravity with a positive cosmological constant. This relation can be inferred from two perspectives. The first one is the investigation of the semi-classical limit of the model via the asymptotics of the amplitude for the three-simplexes (given by a quantum 6j symbol). ... The asymptotics of the quantum 6j symbol has been computed in [43] and yields the cosine of the Regge action with a cosmological term.

An alternative way to relate the Turaev-Viro model to three-dimensional gravity with positive cosmological constant is obtained from the correspondence between three-dimensional gravity, BF theory and Chern-Simons gauge theory. ... The fact that the Turaev-Viro sum of a manifold M is equal to the modulus square of the Reshetikhin-Turaev invariant of M, relates the Turaev-Viro state sum to BF theory with a positive cosmological constant"

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#### Finbar

No, what he's saying is that if there is matter and nongravitational interactions at scales $$E \ll M_P$$, then at $$E \sim M_P$$ these interactions remain and, furthermore, their couplings are of order unity. There is therefore no regime where pure gravity exists in the presence of other interactions. There are further arguments in http://arxiv.org/abs/hep-th/0601001 that gravity is always the weakest force in such a scenario.

This is an important concept when we ask about how to quantize gravity in a real-world scenario. Whether or not there are quantum theories of pure gravity as toy models remains an interesting question, but perhaps not one that is completely relevant to describing our universe.
Yes i agree that to make contact with reality we must couple gravity to matter. But there is nothing he says that suggests we have to unify the forces to obtain a consistent theory which is what you implied. There's a big difference between unification and coupling.

#### suprised

If string theory is any right, then it seems that pure gravity is not consistent at higher loop orders. In order to have a modular invariant partition function, and thus a unitary theory, extra degrees of freedom (compactified extra dimensions for example) appear to be necessary.

This may be a good testing ground between strings and LQG: can the loopy people construct a consistent quantum theory of pure gravity? It would be interesting to see whether a constraint on matter appears in their framework or not, eventually.

#### atyy

If string theory is any right, then it seems that pure gravity is not consistent at higher loop orders. In order to have a modular invariant partition function, and thus a unitary theory, extra degrees of freedom (compactified extra dimensions for example) appear to be necessary.

This may be a good testing ground between strings and LQG: can the loopy people construct a consistent quantum theory of pure gravity? It would be interesting to see whether a constraint on matter appears in their framework or not, eventually.
I think there are quite a few LQG people who are thinking in the direction that pure gravity cannot work. On the more conservative end, there is LQC which seems to always incorporate matter, and on the less conservative end, there is the idea explored Freidel, Livine, Oriti, Ryan and others that unification should take place. Also, Freidel and Krasnov have tried to make links to AdS/CFT. This is all very piecemeal, but it indicates diversity in the LQG community (loss of direction;).

OTOH, even though the handwavy arguments indicate that pure QG won't get the BH right, Polchinski's text still acknoweldeges Asymptotic Safety as not having been formally ruled out. I think the most interesting result in this direction is that of Causal Dynamical Triangulations, which seems to have a ground state that is like a de Sitter universe.

#### marcus

Gold Member
Dearly Missed
...
This may be a good testing ground between strings and LQG: can the loopy people construct a consistent quantum theory of pure gravity? ...
I'm not sure what you mean. The current review of the status of the program discusses the inclusion of matter---I assume that has always been the goal. Some progress on including matter has been made recently as reported at the end of http://arxiv.org/abs/1102.3660 .

Currently quite a lot of effort in that direction, some attempts Atyy mentioned plus the recent Rovelli et al "Spinfoam Fermions". Will it be successful? No one can say.

The most recent broad audience review of the Loop program is http://arxiv.org/abs/1012.4707 . That is easy to read and would also discuss progress on including matter.

By including matter I don't mean incorporating a detailed version of the standard model, as I expect everyone understands. Rather more modestly, one wants to see how fermion degrees of freedom should inhabit the geometry as represented by the network or cell-complex (i.e. foam).

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#### atyy

I'm not sure what you mean. The current review of the status of the program discusses the inclusion of matter---I assume that has always been the goal. Some progress on including matter has been made recently as reported at the end of http://arxiv.org/abs/1102.3660 .

Currently quite a lot of effort in that direction, some attempts Atyy mentioned plus the recent Rovelli et al "Spinfoam Fermions". Will it be successful? No one can say.
Well, the question is does it require matter to be consistent? A very long line of LQG thought, right through and embodied by the Zakopane lectures is that even though matter can be incorporated (and ultimately must be to make an experimental prediction), it is not needed.

#### marcus

Gold Member
Dearly Missed
That's very interesting Atyy, but the actual direction of current researh involves the inclusion of matter, both in the full theory (Rovelli et al Spinfoam Fermions paper) and most actively in the application to cosmology. I don't know about "very long line of thought". Pragmatically what matters is what people do, not what they you or I think about it. Or am I mistaken about this?

#### atyy

That's very interesting Atyy, but the actual direction of current researh involves the inclusion of matter, both in the full theory (Rovelli et al Spinfoam Fermions paper) and most actively in the application to cosmology. I don't know about "very long line of thought". Pragmatically what matters is what people do, not what they you or I think about it. Or am I mistaken about this?
I think you are mistaken. For example, up to the point where, as you like to say, Rovelli says "This is the theory", there is no matter (as interpreted by him), indicating that he believes there can be a consistent theory without matter.

(My suspicion is he is near a consistent theory, but one that does not contain pure gravity - but CDT rebuts this argument, so I am curious).

#### marcus

Gold Member
Dearly Missed
...(My suspicion is he is near a consistent theory, but one that does not contain pure gravity - but CDT rebuts this argument, so I am curious).
We may never know, since by the end of the papers you mentioned he is already talking about how to include matter. In the selfsame theory (and the progress towards it that has recently occurred.)

Theories are made to be tested: that will happen and decide. The rest is academic.

You pointed out to me that the bridge between the full theory and CMB cosmology is still not complete. It has only reached a "halfway" stage that still employs a manifold but has more degrees of freedom (including some anisotropy/inhomogeneity) than the old LQC did.

I'd guess that completing that bridge is the most urgent item on the agenda (because it leads to a test of the full theory by CMB observations, not just a test of the Loop cosmology application.)

#### atyy

No, it's clear. Otherwise the semiclassical limit having Regge-like terms is wrong.

#### marcus

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No, it's clear. Otherwise the semiclassical limit having Regge-like terms is wrong.
I don't understand Atyy. I guess you need to use more words with me and explain a bit more. What is clear? Don't mind if you think you are repeating the obvious, just spell it out.
Can you point me to an equation in 1102.3660 which would be wrong if such and such were the case? I know that there is a discussion of semiclassical limit and that the Regge action appears there.

Could you be talking about eqn 101 on page 18? I wonder what would make that eqn wrong? But basically what is "it" that you say is clear? Sorry for any slow lumberingness.

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#### atyy

It's clear that Rovelli intends to quantize pure gravity. In his words "Loop quantum gravity is resolutely a theory of quantum gravity that does not address the unification problem." http://arxiv.org/abs/1012.4707 p7

#### marcus

Gold Member
Dearly Missed
It's clear that Rovelli intends to quantize pure gravity. In his words "Loop quantum gravity is resolutely a theory of quantum gravity that does not address the unification problem." http://arxiv.org/abs/1012.4707 p7
I see part of what you are saying. According to you a theory which includes matter can still be "pure gravity".
All it has to do is allow matter to ride in the geometry and take part in gravity---but not encorporate the standard model generation, particle interactions etc. Then it is still "pure".

It can have all the matter it wants as long as it does not "address the unification problem", as Rovelli puts it. And in the same paper he discusses including fermion fields into the spinfoam picture. Resolutely, one might say

#### Sardano

Some of you are saying that LQG includes "matter fields". Ok, but for me this is a joke. Is this "matter content" of the lagrangian the Satandard Model or any kind of matter content that includes the Standard Model?. If the answer is yes: then okey, LQG still have a chance of being correct. Is the answer is no, then LQG has nothing to say and Enriques argument still apllies. I have heard that LQC "resolves" the Big Bang into a Big Bounce. Please, dont make me laugh, because the matter content of such theories is ridiculous, like putting just a scalar.

#### mitchell porter

Three threads on 3D gravity, I don't know where I should post!

In http://physics.stackexchange.com/questions/6393/can-a-cft-2-which-cant-be-factorized-into-chiral-and-antichiral-parts-and-or-h" [Broken], Moshe Rozali says of Witten's "Three-dimensional gravity revisited": "I was wondering also what is the impact of this paper on the community of people playing with gauge theory formulations of pure gravity (in 3 and 4 dimensions). This should really give them a pause, since 3dim pure gravity is the most common toy model for them." The thread itself is about how a technical conjecture of Witten's in the paper is wrong, but I believe Rozali is referring to the introductory remarks, in which Witten says his own earlier work on 3D gravity as Chern-Simons theory was wrong.

Personally, I am torn on whether to engage with this issue. I can see a way forward: We compare the "Turaev-Viro model" - about which I know nothing, but which is serving in these threads as the exemplar of pure 3D gravity (is it "canonically quantized gravity"?) - with Witten's pure 3D gravity in AdS. We can exhibit the mathematical guts of both "theories", and try to compare them. This can be done - at least, I believe I understand Witten's paper - it just requires a bit of hard work. I'm reluctant to take the lead, but I could be induced into a dialogue if someone (atyy?) wants to talk about how Turaev-Viro works or has questions about Witten's paper.

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#### atyy

Three threads on 3D gravity, I don't know where I should post!

In http://physics.stackexchange.com/questions/6393/can-a-cft-2-which-cant-be-factorized-into-chiral-and-antichiral-parts-and-or-h" [Broken], Moshe Rozali says of Witten's "Three-dimensional gravity revisited": "I was wondering also what is the impact of this paper on the community of people playing with gauge theory formulations of pure gravity (in 3 and 4 dimensions). This should really give them a pause, since 3dim pure gravity is the most common toy model for them." The thread itself is about how a technical conjecture of Witten's in the paper is wrong, but I believe Rozali is referring to the introductory remarks, in which Witten says his own earlier work on 3D gravity as Chern-Simons theory was wrong.

Personally, I am torn on whether to engage with this issue. I can see a way forward: We compare the "Turaev-Viro model" - about which I know nothing, but which is serving in these threads as the exemplar of pure 3D gravity (is it "canonically quantized gravity"?) - with Witten's pure 3D gravity in AdS. We can exhibit the mathematical guts of both "theories", and try to compare them. This can be done - at least, I believe I understand Witten's paper - it just requires a bit of hard work. I'm reluctant to take the lead, but I could be induced into a dialogue if someone (atyy?) wants to talk about how Turaev-Viro works or has questions about Witten's paper.
I don't think we can compare the Turaev-Viro model and Witten's paper, or at least if we compare them, they are about different physical systems.

My understanding of Witten's paper is that it's about 3D quantum gravity with negative cosmological constant. He essentially retracts his earlier proposal that this is described by a Chern-Simons quantum theory, and makes a new proposal that it is described by a certain CFT.

The Turaev-Viro model is a spin-foam model. It is related to the Ponzano-Regge model which is a spin-foam model that uses normal groups, and is supposed to describe 3D Euclidean quantum gravity. The Ponzano-Regge model is divergent. The Turaev-Viro model (which apparently wasn't originally intended for gravity) replaces Ponzano-Regge's normal groups with quantum groups, and becomes finite. The quantum group seems to lead to a positive cosmological constant.

So I think the TV model has a Euclidean bulk with positive cc, but I presume Witten has a Lorentzian bulk with negative cc.

Some of the things I don't understand about the TV model are:
1) What is a good semiclassical limit for pure 3D quantum gravity?
2) Does the TV model have that limit?

Mizoguchi and Tada http://arxiv.org/abs/hep-th/9110057 examined that limit and concluded maybe it wasn't really gravity: "Therefore it would be better to consider the Regge action appeared in our model as the CS action, rather than the Einstein action. The strange i factor may indicate the subtlety in the correspondence between the Euclidean gravity and a CS theory."

Looking at the thread you linked to, it seems Witten's conjecture is wrong. So there is no known definition of pure 3D quantum gravity in AdS. And from Mizoguchi and Tada, the TV model also doesn't describe 3D quantum gravity with positive cc. It's funny how alluring (but misleading?) the similarity with Chern-Simons.(The TV model seems to have a much tighter link to the Levin-Wen models than to 3D gravity.)

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