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Is there any evidence of ultraviolet quantumness and well defined behaviour in eleven dimensional supergravity? Of course, since it is one limit of M-theory, I see no good review of this topic in the literature. So, my question is:

  1. Is quantum theory for 11d SUGRA a well defined theory?

  2. What are the arguments for a finiteness in this theory? Along the time, there has been pros and contras against it, since it seems not to describe the real world.

Related, but not important in the answer, is 11d SUGRA able to develop dS like solutions? After all, it seems we live in a dS (or almost de Sitter) Universe, and the theory seems to predict, like many other theories, a wrong sign for the cosmological constant. Is it a proof of its failure? Or, is there any hope to find solutions in 11d SUGRA to approach the real Universe after compactification?

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