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Does string theory gravitons have 4D GR as its low energy limit?

  1. Oct 23, 2007 #1
    Lisa Randall said "string theory reproduces GR in 10 dimensions"

    Does string theory gravitons have 4D GR as its low energy limit?

    I know that its lowest mode vibrations corresponds to a massless spin-2 particle, the graviton. I know GR in 4D can be extended with susy.

    Does it reproduce all experimentally proven features of 4D GR including time dilations and spacetime curvature and varying time?

    Criticisms I have heard is that 1- it has not been proven to be finite beyond 2-loop level by Phong and 2- the series does not summate to a finite number, it comes close to values given by GR but then diverges 3- the series is not borel summable, 4- the series when added to infinity become infinite rather than finite, 5- it is not background independent whereas GR is, 6- SUSY gravity in 10 or 11D is very different than GR in 4D.

    It is alleged that a quantum theory of gravity must have gravitons as the quanta of gravity, and only string theory allows gravitons to interact to produce renormalizable results. Gravitons done in QFT are nonrenormalizable.

    Does LQG gravitons renormalizable?
  2. jcsd
  3. Oct 23, 2007 #2
    Well, if string theory is right, then we DO live in ten dimensions, and GR in ten dimensions is exactly what we need.
  4. Oct 23, 2007 #3
    What has been tested is GR in 4D, and I wonder if every aspect of GR that has been experimentally established can be reproduced in string/M-theory, after 6-7 dimensions have been compactified and SUSy broken.
  5. Oct 23, 2007 #4


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    From the point of view of our scales, yes they should be experimentally indistinguishable.

    From a fundamental pov. its not quite minimal GR, but really supergravity + some compactification residuals + a few other objects (like the Dilaton) etc

    All those things tend to go to zero or limit to plain GR for an observer doing experiments with our normal everyday experimental apparatuses (for instance solar system tests).
  6. Oct 24, 2007 #5
    The canonical GR predictions (curved space-time, perhilion of mercury, gravitational lensing, etc.) are not affected by string theory. Someone correct me, but I think that stringy corrections to gravity are so small that we can't really hope to test them. The types of ``residuals'' that get left over depend pretty crucially on the compactification. So to leading order, I think string theory DOES reproduce GR in 4d. Beyond leading order may not be testable, because the corrections probably go as E/M, where M is the Planck mass.
  7. Oct 24, 2007 #6
    * The graviton is expected at some level of a quantum theory of gravity since we expect a quantum field theory to describe interactions at low energies. (But the issue of the fundamental nature of spacetime geometry is up in the air, and gravitons are not fundamental quanta in the various formulations of non-perturbative quantum gravity.) With regard to observational consistency, the issue of whether or not there are gravitons is irrelevant. Also, gravitation in QFT is still an open issue: at least with supersymmetries, our understanding of the finiteness of various higher order terms is still weak.
    *Does string theory reproduce GR at low energies? Not in the sense of finding an actual low energy effective theory, since these are harder to come by in string theory. But the truncation to the string tree level (interactions without intermediate splittings) and to massless string states "gives supergravity theories" (i.e. the interactions of states we see in those sugra theories). Sorry to get a bit technical here, but: The "emergence of GR" is not obtained by considering some sort of coherent state of strings to find spacetime backgrounds, but rather, the supergravity equations of motion appear as constraint equations that the string worldsheet theory must satisfy.
    * As has already been mentioned, you can consider string theories (or "M" theory for that matter) in which the low energy theory looks 4-dim...and it's easy to get a lot of features consistent with current observations...but string theory is a very large and flexible framework when it comes to this, so now it's not so surprising.
    * It does not reproduce all observations in the sense that we have not yet found a particular "phase" of the theory in which things as important as the correct cosmological constant is found, along with the correct parameters in the standard model of particle physics.
    * Your list of the criticisms are correct: the finiteness of perturbative string amplitudes to all orders is not a proof, but a claim; the full series appears to be not Borel summable, which is related to your "divergence" point (though many stringists would say it's not so big a deal since it's an artifact of working in the perturbative framework); there isn't a definite framework for "non-perturbative string theory" that is background independent in the sense that GR is (many stringists don't see this as a big deal and think relativists play gravity up too much).
    * There is the major criticism, as touched upon above and in a previous post, that there is no strong argument that string theory is a falsifiable theory. Actual "stringy" behavior is presumed to be observable at energy scales outside of possible measurement. There are scenarios in which this behavior (or at least quantum gravity effects) could be seen at lower energy scales...but only that class of scenarios, and not the framework of string theory, are falsifiable.
    * So there are many interesting features of string theory...we are still trying to understand QFTs (!!), and while string theory has certainly helped there as a calculational tool, its promise as a physical theory is on thinning ice, I believe.
  8. Oct 24, 2007 #7
    This will start a riot, but nonetheless: No, string theory does not "predict" or "reduce to" classical general relativity in any limit. As of yet, no counterpart to the Hamiltonian constraint of classical GR has been predicted by string theory so, in my opinion, claiming that string theory reduces to GR in some limit is, at best, disingenuous.

    Even leaving aside the question of the Hamiltonian constraint, there are all sorts of predictions and indications made by classical GR which it is difficult if not impossible to see produced by a string theory: background independence, the implication of a timeless physics by the WdW equation, and so on and so on.

    Of course, string theorists (particularly students) will generally not concede any of these points since a solid understanding of GR has long since seemed to stop being a prerequisite of a good grad education.
  9. Oct 24, 2007 #8


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    That doesn't make any sense, supergravity is easily shown to reduce to general relativity at least with a Vielbein or in a weak field (eg it reproducing Einsteins equations).

    As far as cosmological solutions, the WdW equation is a semiclassical object, it is absolutely not predicted by general relativity. No one knows what that black box holds or if its even correct or not. Afaik, some string theory cosmological solutions do make contact with the WdW eqn, but they should be looked at with skepticism, not as a plus.

    Whether such and such a formalism is manifestly BI or not is a seperate issue (and a tired one at that). Its trivially easy to formulate GR in such a way that it breaks background independance, even though you know that it carries the property deep down even if its hidden. Its very easy to mask or hide symmetries of a theory (for instance simply gauge fix).

    As far as the Hamiltonian constraint and what ST says about it, on this I am silent. I do not know the answer to this, maybe someon else does
  10. Oct 25, 2007 #9


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    I am particularly interested in that issue. If the above is correct, then what exactly the relation between graviton string states and background spacetime metric is? The textbooks on string theory (GSW, Polchinski) are (for my taste) too superficial on that. Do you know a reference where that issue is studied more carefully? (The case of bosonic strings would be fine as well.)
    Last edited: Oct 25, 2007
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