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Many quantum-gravity theories are strongly interacting. It is not clear if they produce the gravity as we know it at low energies. So I wonder, is there any quantum-gravity theory that

a) is a well defined quantum theory at non-perturbative level (ie can be put in a computer to simulate it, at least in principle).

b) produces nearly flat space-time.

c) contains gravitons as the ONLY low energy excitations. (ie the helicity $\pm 2$ modes are the ONLY low energy excitations.)

We may replace c) by

c') contains gravitons and photons as the ONLY low energy excitations. (ie the helicity $\pm 2$ and $\pm 1$ modes are the ONLY low energy excitations. This is the situation in our universe.)

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  • $\begingroup$ Hi Prof. Wen, and welcome to Physics Stack Exchange! The edit you made to this answer is the sort of thing that should be a comment. You didn't have enough reputation to comment on that answer at the time, but now you do (it takes 50), so I thought you might want to go back there and leave your thoughts as a comment. $\endgroup$
    – David Z
    Commented May 27, 2012 at 5:19
  • $\begingroup$ Requiring the theory to be non-perturbative narrows the field a lot. I think it leaves only Loop Quantum Gravity and Causal Dynamical Triangulations, neither of which satify your requirements (b) and (c). $\endgroup$
    – John Rennie
    Commented May 27, 2012 at 9:25
  • $\begingroup$ I wonder if the matrix model can produce a), b) and c). We have two lattice models that have a) and c) by assuming b). $\endgroup$
    – Xiao-Gang Wen
    Commented May 27, 2012 at 10:41
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    $\begingroup$ @JohnRennie: That is false, you have string theory matrix models and AdS/CFT models which are nonperturbatively complete. The LQG stuff is not clearly correct, there is a vacuum stability issue that is not adressed (as far as I can see) which is protected by SUSY in strings, and CDT is not a theory as far as I know. Is there a reference? $\endgroup$
    – Ron Maimon
    Commented May 28, 2012 at 5:44
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    $\begingroup$ @drake: I don't know a reference, but here is an argument: there are vacuum stability issues in non-SUSY gravity which aren't fixed by a discretization, since they are in the continuum theory. For example, Witten's bubble-of-nothing instantons make the SUSY-less KK vacuum unstable, even though you would never guess from the naive quantization of the theory. Similarly, if you do LQG on a KK circle. There is nothing in LQG that guarantees a near-flat infinite vacuum is completely stable either. It might be anyway, but I don't think so. $\endgroup$
    – Ron Maimon
    Commented Aug 3, 2012 at 18:07

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A well-defined quantum theory is clearly presented by Rovelli in the 2011 Zakopane lectures: http://arxiv.org/abs/1102.3660

It definitely satisfies your criterion A, easily seen to heuristically give B, and I do not know personally what is the status of C, but I know that a graviton propagator is definable and computable, which might be sufficient.

Personally, I believe there is a lot of underlying commonality with your own work (which I follow with a dilettantish interest). In particular, Rovelli has also introduced fermion and gauge theory coupling by means of lattice field theory living on a quantum graph, which to my mind resembles string-nets: http://arxiv.org/abs/1012.4719

There are also a nice set of recorded lectures at the Perimeter (perhaps you've already seen them in person, however), which contains a lot of colloquial talking which helps to fill in between the lines, and which I think expresses Rovelli's personal view of the state of the research much better than his written work: http://pirsa.org/C12012

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    $\begingroup$ Zakopane lectures is very readable. Thank you very much. I will study it. $\endgroup$
    – Xiao-Gang Wen
    Commented May 28, 2012 at 0:44
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    $\begingroup$ This is a reasonable answer, but the Rovelli theory is not clearly an example. I read through this paper when you pointed it out, and it is only clear that it is an approximate triangulation of the Einstein action, but there is no guarantee that the flat vacuum is stable. The continuum Einstein action is not positive definite, and the fact that you have an interpretation of the spin-networks in LQG as approximate triangulations of Einstein action does not mean that the flat space corresponds to a true vacuum wave-functional for the spin-network (although it does suggest this). $\endgroup$
    – Ron Maimon
    Commented May 28, 2012 at 5:46
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    $\begingroup$ Sen has recently and IMHO rather convincingly shown that LQG does not have an obvious interpretation as a gravitational theory: The leading logarithmic correction to the area law which one computes in LQG does not match the number one computes using only low energy arguments. This suggests that the current formulations of LQG don't have a classical gravity limit. $\endgroup$
    – user1504
    Commented May 28, 2012 at 20:37
  • $\begingroup$ @RonMaimon: sorry --- ambiguous statement there. The adverb "clearly" is referring to the paper by Rovelli --- I think he has written a clear paper. I don't not know if it really satisfies Prof. Wen's criterion. $\endgroup$
    – genneth
    Commented May 28, 2012 at 22:46
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    $\begingroup$ @Genneth: The "Spinfoam fermions" paper is very interesting. However, when we study string-net models, our main motivation is to find a unified origin of gauge theory and Fermi statistics from a model that contains ONLY simple qubits. $\endgroup$
    – Xiao-Gang Wen
    Commented Jun 19, 2012 at 12:48
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I think the answer to your question is "No."

String theory seems closest to me, since one can formulate it in terms of matrix models, which resemble models we do know how to simulate. One can also make computations in this fashion which match with supergravity computations (e.g., Robert Helling's early work). I'm not sure, however, that it's known precisely how one would express a Standard Model computation in terms of matrix models variables.

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  • $\begingroup$ It's not definitively no (unless you only count published vacua, then it's probably no). The main issue is that you'll get gravitinos in a SUSY compactification, so the restriction to only gravitons means you need a non-SUSY vacuum, and this is why there aren't examples. You need to project out the SUSY and keep zero cosmological constant, and have no emerging fermions and only confined gauge fields. That's a tough set of constraints. $\endgroup$
    – Ron Maimon
    Commented May 28, 2012 at 22:35
  • $\begingroup$ @Ron: What you say is true. Whether or not "No" or "No, not at present" is a better answer depends on what you think the meaning of "is" is. $\endgroup$
    – user1504
    Commented May 29, 2012 at 0:55
  • $\begingroup$ ok, +1, just checking we're on the same page. $\endgroup$
    – Ron Maimon
    Commented May 29, 2012 at 3:55
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Asymptotically Safe Gravity (if it exists) should have that pretty much by definition: In the low energy limit it reproduces the Einstein-Hilbert action which has flat space as a solution around which you can consider small perturbations, in the high energy limit you run to the fixpoint.

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  • $\begingroup$ Thanks for the link which discussed the definition in detail. But the point is that "Is there a quantum model that satisfies a) [and produces b) and c)]?" $\endgroup$
    – Xiao-Gang Wen
    Commented May 27, 2012 at 12:11
  • $\begingroup$ @Xiao-GangWen: I agree --- in its present state, AS gravity is not effectively computable. $\endgroup$
    – genneth
    Commented May 27, 2012 at 22:57
  • $\begingroup$ Look, I've read a bunch of your papers, so I know you're in the emergent gravity part of things. But your question is really vague on what you mean with "produce" a flat space limit. ASG in the low energy limit has the metric as dof and that has in the simplest case a flat space solution and its excitations are gravitons. It's not in conflict with emergent scenarious. That it's not "effectively computable" is a different issue altogether and one that wasn't mentioned in your question. $\endgroup$
    – WIMP
    Commented May 28, 2012 at 7:09
  • $\begingroup$ I purposely made a vague statement in (b), since different approaches may have different ways to "produce" naturally the nearly flat space-time. One natural way is that the flat space-time corresponds to the ground state of the quantum system as defined by (a). $\endgroup$
    – Xiao-Gang Wen
    Commented May 28, 2012 at 8:04
  • $\begingroup$ Well, ASG "naturally produces" a nearly flat space time in the low energy limit because it reduces, by construction, to General Relativity plus small perturbations. Which is, of course, perturbatively non renormalizable, but that doesn't have to bother you in that case which is the whole point. That having been said, whatever the high energy completion looks like in the ASG scenario, it fulfills your requirements. $\endgroup$
    – WIMP
    Commented May 28, 2012 at 9:50

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