I'm not sure a lot is known. The various string theories--which are M-theory dimensionally reduced in various ways--have to have a spacetime given to them, as opposed to the background falling out of the equations like how Minkowski spacetime is a solution of GR.
11d supergravity--the low energy limit of M-theory--has an SO(10,1) type spacetime. But who knows what's going on in M-theory.