Supermembranes

Supermembranes are hypothesized objects that live in the 11 dimensional theory called M-Theory and should also exist in 11 dimensional supergravity. Supermembranes are a generalisation of superstrings to another dimension. Supermembranes are 2-dimensional surfaces. For example, they can be spherical or shaped like a torus. As in superstring theory the vibrations of the supermembranes correspond to different particles. Supermembranes also exhibit a symmetry called supersymmetry without which the vibrations would only correspond to bosons and not fermions.

The energy of a classical supermembrane is given by its surface area. One consequence of this is that there is no difference between one or two membranes since two membranes can be connected by a long 1 dimensional string of zero area. Hence, the idea of 'membrane-number' has no meaning. A second consequence is that unlike strings a supermembrane's vibrations can represent several particles at once. In technical terms this means it is already 'second-quantized'. All the particles in the Universe can be thought to arise as vibrations of a single membrane.

When going from the classical theory to the quantum theory of supermembranes it is found that they can only exist in 11 dimensions, just as superstrings can only exist in 10 dimensions. When examining the energy spectrum (the allowed frequencies that a string can vibrate in) it was found that they can only be in discrete values corresponding to the masses of different particles.

It has been shown:

At first the discovery that the spectrum was continuous was thought to mean the theory didn't make sense. But it was realised that it meant that supermembranes actually correspond to multiple particles. (The continuous degrees of freedom corresponding to the coordinates/momenta of the additional particles).

The action for a classical membrane is simply the surface area of the world sheet. The quantum version is harder to write down, is non-linear and very difficult to solve. Unlike the superstring action which is quadratic, the supermembrane action is quartic which makes it exponentially harder. Adding to this the fact that a membrane can represent many particles at once not much progress has been made on supermembranes.

It has been proven that the low energy vibrations of the supermembrane correspond to the particles in 11 dimensional supergravity.

...
Wikipedia