Again, Is N=8 Supergravity Finite?

The main argument generally given for working on string theory is that it’s the only way to get a finite theory of quantum gravity. One often hears claims that gravity can’t be quantized using QFT, that string theory is needed to “smooth out the violent space-time fluctuations at the Planck scale”, or some such explanation for the inherent non-renormalizability of quantum field theories of gravity. From the earliest days of their study, it was hoped that supergravity theories would have better renormalizability properties, with the maximally extended supergravity, N=8 supergravity, the most likely to be well-behaved.

For years the general belief has been that N=8 supergravity is non-renormalizable, based on the existence of possible counterterms at high enough order. The problem has always been that calculating the coefficients of these counterterms is too difficult, so one cannot be sure that one would not get zero if one actually did the calculation. Last year I wrote here about a talk by Zvi Bern in which he mentioned that twistor space methods for doing these kind of calculations were giving indications that these coefficients might be zero. Tonight there’s a new paper out by Green, Russo and Vanhove suggesting the same thing. Their arguments involve M-theory and consistency conditions relating supergravity and the low energy limit of 10-d superstring theory.

It would be quite remarkable if it turns out that this work by Michael Green, using string theory and M-theory techniques, ends up shooting down the main argument for why one has to abandon QFT if one wants to do quantum gravity.

Update: Next month at UCLA there will be an entire workshop devoted to this question, entitled Is N=8 Supergravity Finite?

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12 Responses to Again, Is N=8 Supergravity Finite?

  1. anon. says:

    “It would be quite remarkable if it turns out that this work by Michael Green, using string theory and M-theory techniques, ends up shooting down the main argument for why one has to abandon QFT if one wants to do quantum gravity.”

    I don’t see that they would shoot down the argument; one has to be able to break SUSY without reintroducing nonrenormalizability. String theory allows one to have reasonable, realistic soft SUSY breaking. I’m not sure that N=8 SUGRA can do that.

    (Not that the question isn’t interesting, and I would be happy to be corrected with pointers to references!)

  2. arnold says:

    a “naive” question. Why is it so important that there are no divergencies in a quantum theory of gravity?

  3. anon. says:


    That isn’t precisely what’s important — the technical property is “renormalizability”, which means essentially that the theory is completely specified by a finite number of constants. Certain divergences are OK in a renormalizable theory, but in gravity they are usually too severe. One would need infinitely many parameters to quantize general relativity naively, and hence one would not really have a theory. You would always know at most finitely many parameters, and thus could never actually calculate anything.

  4. A.J. says:


    One other reason that anon. didn’t mention: The sort of divergences that appear when you try to quantize classical GR and supergravity have appeared elsewhere, e.g. in Fermi’s theory of the weak interaction. (Although gravity is a considerably more broken theory than Fermi’s ever was.) They usually indicate that the degrees of freedom we’ve chosen — in this case, gravitons — might not be valid at arbitrarily high energies.

  5. Kea says:

    I don’t see much evidence of them taking the MHV twistor techniques seriously, so this paper can’t have much to do with that excellent talk by Zvi Bern.

  6. MathPhys says:

    Why can you softly break SUSY in a string theory, but not in a finite supergravity theory?

  7. arnold says:

    thanks anon and a.j.

    Let me try to explain again my doubt : in any theory one has all possible operators allowed by symmetries, whose coefficients have to be fixed at some energy scale by experiments.

    Now, why does it matter if this coefficients are divergent or not?

  8. Gordon says:

    I have about 8 papers on derivative corrections in IIB superstring
    theory and N=8. Including some matlab code that computes the
    coefficients. You might find this one interesting:

    On the finiteness of N=8 quantum supergravity.
    Gordon Chalmers (Argonne) . ANL-HEP-PR-00-83, Aug 2000. 11pp.
    e-Print Archive: hep-th/0008162

  9. Gordon says:

    By the way I have completed software in matlab that allows for
    loop calculations of amplitudes. I dont plan on publishing all of
    them for a while. Available on request for various theories.

  10. Gordon says:

    Recent article by Green, Russo, and Van Hove:

    hep-th/0611273 [abs, ps, pdf, other] :
    Title: Ultraviolet properties of Maximal Supergravity
    Authors: Michael B. Green (Cambridge U., DAMTP), Jorge G. Russo (ICREA, Barcelona & Barcelona U., ECM), Pierre Vanhove (Saclay, SPhT)
    Comments: 10 pages

    (reproduces my earlier arguments)

  11. Johny says:

    Gordon: (reproduces my earlier arguments)

    Yet, they don’t seem to cite you.

  12. Gordon says:

    Well, Johny, it only took about 6 years and then sum.

    Lets cite it then. I do.

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