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The formulation of String theory is fairly straight forward in that the action is just the world-sheet area of a string. Then you can add supersymmetry in various ways. Finally you add some ghosts to get rid of over counting of states. You find the whole thing only works in a certain number of dimensions preserving both world-sheet and space-time symmetries.

So why is M(embrane) theory so difficult to formulate? If one replaces closed strings with closed membranes, should it not be straight forward (in theory) to go through the same process?

Which part of the theory is making it difficult? Is it the supersymmetry? The over counting of states? Non-linearlity? The difficulty of counting membrane topologies?

Is it absolutely certain that M-Theory is based on the world-sheet volume of membrane histories in the same way that string theory is based on world-sheet areas of string histories? Or is it based on something that resembles membranes but not quite (such as fuzzy membranes or something).

And do we know for certain that a Membrane theory must also contain 5-branes for it to be consistent?

Basically, what is the stumbling block?

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  • $\begingroup$ Conformal symmetry is much more powerful in 2d than in more than 2d. $\endgroup$
    – user2309840
    Commented Dec 8, 2015 at 16:21
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    $\begingroup$ Related: physics.stackexchange.com/q/55431/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Dec 8, 2015 at 16:22
  • $\begingroup$ The difficulty isn't in formulating the membranes, which exist even in the 10-dimensional string theories (in certain formalisms, anyway). The difficulty in formulating M-theory is that in its definition it's a theory which gives the Heterotic E and Type IIA string theories respectively when compactified on a line segment and circle respectively. 10-dimensional string theories were derived because we could, and some turned out to be remarkably consistent with the Standard Model, while M-theory is to be written based on certain defined properties. $\endgroup$
    – Abhimanyu Pallavi Sudhir
    Commented Jan 1, 2016 at 6:24

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