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Could M-theory be formuated using loop gravity?

  1. Dec 25, 2009 #1
    Smolin and Rovelli and Ashketar point out that loop formalism can be extended to supersymmetry and to higher dimensions.

    Since 11D Supergravity is just a low energy regime of M theory, why not apply and canonically quantize 11D super gravity, in flat space susy unbroken.

    The result are spin networks that carry more labels.

    Then use a variety of semiweave states to build a 4D spacetime, possibly broken SUSY. No need to do a landscape.

    The spin networks are the quantized product of 11D Susygravity, which are then used to build a 4D spacetime, with strings.
  2. jcsd
  3. Dec 25, 2009 #2


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    How would you build strings from spin networks? I don't think it's possible to do that.
  4. Dec 25, 2009 #3
    I was thinking of building lqg spacetime for strings to move across. The susy 11 dimensions required by string theory become extra labels on spin networks, that can produce 4D spacetime.
  5. Dec 29, 2009 #4


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    It's the space of solutions of M-theory that is equiped with the landscape; so w/o being able to construct the 11d solutions for LQG you are not able to say if there will be a landscape or not. In addition it will be hard to dynamically (!) compactify the additional space dimensions. In M-theory the solutions are classical vacua, in LQG nobody is able to separate the classical vacuum from the dynamics (the LQG community says that this background independence is a feature, not a problem of the theory)

    Nevertheless, some time ago I saw a paper on arxiv where they tried to quantize SUGRA according to LQG methods including fermion fields. I have to check arxiv again ...
  6. Dec 30, 2009 #5
    Start with 11D SUGRA. Reformulate in Ashketar variables then quantize it. Take a semiclassical limit and show 10D strings have the correct behavior as on classical spacetime. Show that the compactification of 11D spinfoams leads uniquely to 4D spacetime.

    Perhaps the landscape problem in strings is the result of envisioning a need to compactify classical space dimensions, perhaps the degrees of freedom exist in a spin network, with SUSY, that can give rise to 4D classical spacetime uniquely.
  7. Dec 30, 2009 #6


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    - complicated - but will certainly work.

    - unfortunately not known for 4d LQG; 11d LQG will not be less complicated :-)

    - how do you want to compactify LQG? compactification means that you use a classical manifold which you can compactify; but in LQG there is no such manifold.

    A manifold may emerge semiclassically, but certainly not at the Planck scale. In addition a spin network need not really have a dimension; again this may be an emergent but not a fundamental concept. So in essence I do not see how you can compactify a theory w/o having a manifold at hand. But as soon as you have derived the manifold in LQG there is no need to compactify it.

    But there is one interesting idea: If you start with 4-dim spin foams you find a theory with spectral dimension = 4 at large scales and spectral dimension = 2 at small scales. What will happen if you start with N-dim spin foams? what will be the large- and the small-scale limit, respectively? Could it be that regardless from which dimension you start, you will always end up with the same scaling behaviour?
  8. Dec 30, 2009 #7
    Fascinating question....

    I was thinking that "- unfortunately not known for 4d LQG; 11d LQG will not be less complicated" maybe adding strings by hand will help (as it adds gravitons which are known to be possibly perturbatively finite)

    I wasn't thinking of compactifying LQG at the planck scale but something along the lines you mention, that the degrees of freedom at the planck scale spin network gives rise to unique 4D spacetime, possibly with broken SUSY. Then adding strings.
  9. Dec 31, 2009 #8


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    but why add strings? what do you miss in LQG?
  10. Dec 31, 2009 #9
    strings all the results of string theory of the last 30+ years, including gauge, fermions, graviton

    the hope is that M theories 11 dimensions are quantum mechanical degrees of freedom at planck scale, fractal like, which at large distances gives rise to 1 unique 4d space, not a landscape
  11. Jan 1, 2010 #10


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    So you think that adding "something" to LQG my give you interactions, particles etc. back. Why not let this something emerge from LQG? Perhaps you can add something on top of LQG, but I am afraid that the string- / m-strucures are not really appropriate because they require a classical manifold to life on.

    I think there are new structures still to be discovered in spin networks with only minimal additional input, especially the fascinating idea of braided structures emerging from framed graphs.
  12. Jan 1, 2010 #11

    I don't know if strings can emerge from LQG spin networks, but since a lot of work has been done on M-theory and how it could reproduce both gravitons and SM, and LQG allows for matter couplings and SUSY. Ok, the idea I'm proposing is that "11-dimensions" and SUSY exist as degrees of freedom on spin networks on the planck scale but as a result of scaling that is the reverse of CDT fractal, where in CDT smaller distances lead to scaling to 2D, here scaling leads to 11D, but at dimensions larger than planck, classical 4D manifold uniquely emerges, avoiding the landscape problem.

    I'd like to see more progress in braided structure but it has a long way to go.
    Last edited: Jan 1, 2010
  13. Jan 2, 2010 #12


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    I don't think so; strings seem to be a perturbative artefact of M-theory only. I did not say let strings emerge ... but let something emerge ... :-)

    So that means just "ordinary" SUGRA, but quantized accordig to the spin-network / spin-foams approach; sounds reasonable to do that.

    OK, now I got the point. You expect the 4d spacetime to be the IR scaling limit of the underlying theory.

    This seems to be a fascinatig idea in itself. I think it is worth to study SUGRA on its own (even w/o your approach :-), i.e. w/o any link to strings and M-theory. There are hints that SUGRA may be UV-finite and can therefore be treated like an ordinary QFT. This picture could be completed by a background independent quantization according to LQG.

    But in the approach you are describing there is no need to introduce strings at all; maybe strings fail to be a fundamental description and are only a large-N artefact of some "ordinary" QFT. So keep the approach as simple as possible, avoid strigs and start with 11d SUGRA.

    I have to admit that I am not an expert in these RG applications. But a major obstacle will be that in your approach the theory becomes lower-dimensional in the IR regime; that's exactly the opposite behaviour of all other approaches like LQG, CFT, Horava, indicating that the IR regime shows more dimensions than the UV.

    For me the cebtral idea is to find a theory which uniquely predicts dimensions and interactions. LQG as of today is not able to do that: one can do LQG in any number of space dimensions and one can add any (gauge) interaction. You idea tries to restrict the interactions by SUGRA reasoning

    I fully agree. I do not see that this is a very active and promising research program. Only a few people are working on. w/o a new idea or a seniour LQG researcher starting a new activity not so much will happen - unfortunately. I am not an insider, so I can't really say how promising this idea is, but for me it's the most fascinating idea I have ever seen. Instead of letting gravity emerge from gauge or string interactions here one tries to let all interactions and particles emerge from spacetime.
    What is puzzling for me is that (as far as I understood) framing is derived from quantum deformation of the SU(2) group in order to incorporate a cosmological constant. So the cc seems to be an input rather than a result of the whole story.
  14. Jan 2, 2010 #13
    if you want to do away with strings then why bother in 11 dimensions since there's no evidence for them? 4D is just fine. While on the topic, why bother with SUSY since there's no experimental evidence for that as well. Of course if LHC finds such evidence obviously SUSY should be incorporated. At the moment though evidence is just 4D GR + SM.

    When elementary particles like electrons and photons and neutrinos are put on a LQG/SF spin network, what sort of relationship exists between an electron and a spin network?
  15. Jan 3, 2010 #14


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    You started with strings. I see no evidence for strings, either.

    There are good reasons for SUGRA w/o strings:
    1) in contradistinction to standard gauge theories the number of SUGRAs is restricted, the construction is not arbitrary. In 11d there is only one unique "maximal" SUGRA. Several higher dimensional SUGRAs can be compactified just as string theory. It is of course interesting if such a compactification could emerge dynamically.
    2) as far as I can see the duality between different string theories and SUGRA requires either some limiting procedures (strong coupling - weak coupling; large N) or one has to use the still unexplored M-theory. In that sense all string theories are just approximations to something else. If we speculate that M-theory does not exist, 11D SUGRA could be an exact theory, whereas strings are only approximations.
    3) I guess that all SUGRAs can be quantized according to the LQG approach directly, whereas string theory requires a drastic modification.

    You are right,but you are not able to expalin why 4D GR +SM. You have an infinite "set of theories"! With SUGRA this set becomes finite. In addition gravity may become (perturbatively) renormalizable. If your idea is right, perhaps 4D GR + SM is a kind of fixed point in this space of theories.

    No "relationship". You just take a graph of a spin networkand attach additional "labels" (quantum numbers, intertwiners) to the vertices and edges. These new labels commute with the LQG labels. It is comparable to constructing a lattice gauge theory.
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