I am studying the $S$ duality between 11D supergravity and type IIA superstring theory from Adel Bilal’s paper. The author says:

Of course, eleven dimensional supergravity is not expected to yield a consistent quantum theory. It should only be the low-energy limit of some consistent theory, baptised M-theory.

I don’t understand what this really means. What is a “consistent quantum theory”? And how do we know that 11 dimensional supergravity is the low energy limit of M theory?


1 Answer 1


Essentially the answer is that the eleven dimensional supergravity is non-renormalizable; to be precise, above two loops, the graviton-graviton scattering amplitude is divergent. A nice review on the specifics of maximal supergravity is Kaluza-Klein supergravity.

Some comments to gain intuition about the UV problems in eleven dimensional supergravity:

  1. They only known way to avoid the UV divergences in all known consistent theories of gravity is the UV/IR mixing mechanism of string theory amplitudes (see my answer to this question). Such a mechanism is absent in the maximal supergravity.

  2. Non-perturbative states in its spectrum exist, namely membranes, three-branes and fivebranes. It is known that the worldvolume theory of the M5-brane is always strongly coupled (the moduli space of its parameters is just a point). A consequence of this is that there is no possibilty to derive its physics from a lagrangian theory, in particular not from the lagrangian of the maximal supergravity. Something more is needed.

  3. As in any supergravity, it's not clear that a lagrangian description must be the correct description of the theory at the Planck scale. Again, an unknown UV-regulator (new physics) is needed.

  • 3
    $\begingroup$ Thank you for the detailed answer. My undergrad thesis involves reproducing the Becker sisters' calculation (which uses the Matrix model of M theory) to compute the scattering of D0 branes at two loops and comparing it the result to 11D supergravity. $\endgroup$
    – saad
    Jul 19, 2020 at 7:38
  • 1
    $\begingroup$ It's always a real pleasure. It sounds like a truly wonderful undergraduate thesis, a really nice training on important stuff. Stay curious, and the best of all lucks for your project. $\endgroup$ Jul 19, 2020 at 19:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.