M, Membranes, and OM

We examine the extent to which the action for the membrane of M-theory (the eleven-dimensional construct which underlies and unifies all of the known string theories) simplifies in the so-called Open Membrane (OM) limit, a limit which lies at the root of the various manifestations of noncommutativity in the string context. In order for the discussion to be relatively self-contained, we start out by reviewing why the strings of ten-dimensional string theory are in fact membranes (M2-branes) living in eleven dimensions. After that, we recall the definition of OM theory, as well as the arguments showing that it is part of a larger, eleven-dimensional structure known as Galilean or Wrapped M2-brane (WM2) theory. WM2 theory is a rich theoretical construct which is interesting for several reasons, in particular because it is essentially a toy model of M-theory. We then proceed to deduce a membrane action for OM/WM2 theory, and spell out its implications for the four different types of M2-branes one can consider in this setting. For two of these types, the action in question can be simplified by gauge-fixing to a form which implies a discrete membrane spectrum. The boundary conditions for the remaining two cases do not allow this same gauge choice, and so their dynamics remain to be unraveled.