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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?
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:
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.
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.
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.
