More than just strings

    Another surprising revelation was that superstring theories are not just theories of one-dimensional objects. There are higher dimensional objects in string theory with dimensions from zero (points) to nine, called p-branes. In terms of branes, what we usually call a membrane would be a two-brane, a string is called a one-brane and a point is called a zero-brane.
    What makes a p-brane? A p-brane is a spacetime object that is a solution to the Einstein equation in the low energy limit of superstring theory, with the energy density of the nongravitational fields confined to some p-dimensional subspace of the nine space dimensions in the theory. (Remember, superstring theory lives in ten spacetime dimensions, which means one time dimension plus nine space dimensions.) For example, in a solution with electric charge, if the energy density in the electromagnetic field was distributed along a line in spacetime, this one-dimensional line would be considered a p-brane with p=1.
        A special class of p-branes in string theory are called D branes. Roughly speaking, a D brane is a p-brane where the ends of open strings are localized on the brane. A D brane is like a collective excitation of strings.
    These objects took a long time to be discovered in string theory, because they are buried deep in the mathematics of T-duality. D branes are important in understanding black holes in string theory, especially in counting the quantum states that lead to black hole entropy, which was a very big accomplishment for string theory.

How many dimensions?

    Before string theory won the full attention of the theoretical physics community, the most popular unified theory was an eleven dimensional theory of supergravity, which is supersymmetry combined with gravity. The eleven-dimensional spacetime was to be compactified on a small 7-dimensional sphere, for example, leaving four spacetime dimensions visible to observers at large distances.
    This theory didn't work as a unified theory of particle physics, because it doesn't have a sensible quantum limit as a point particle theory. But this eleven dimensional theory would not die. It eventually came back to life in the strong coupling limit of superstring theory in ten dimensions.
    How could a superstring theory with ten spacetime dimensions turn into a supergravity theory with eleven spacetime dimensions? We've already learned that duality relations between superstring theories relate very different theories, equate large distance with small distance, and exchange strong coupling with weak coupling. So there must be some duality relation that can explain how a superstring theory that requires ten spacetime dimensions for quantum consistency can really be a theory in eleven spacetime dimensions after all.
    Since we know that all string theories are related, and we suspect that they are but different limits of some more fundamental theory, then perhaps that more fundamental theory exists in eleven spacetime dimensions? These question bring us to the topic of M theory.

The theory currently known as M

    Technically speaking, M theory is is the unknown eleven-dimensional theory whose low energy limit is the supergravity theory in eleven dimensions discussed above. However, many people have taken to also using M theory to label the unknown theory believed to be the fundamental theory from which the known superstring theories emerge as special limits.
    We still don't know the fundamental M theory, but a lot has been learned about the eleven-dimensional M theory and how it relates to superstrings in ten spacetime dimensions.
    In M theory, there are also extended objects, but they are called M branes rather than D branes. One class of the M branes in this theory has two space dimensions, and this is called an M2 brane.
    Now consider M theory with the tenth space dimension compactified into a circle of radius R. If one of the two space dimensions that make up the M2 brane is wound around that circle, then we can equate the resulting object with the fundamental string (one-brane) of type IIA superstring theory. The type IIA theory appears to be a ten dimensional theory in the normal perturbative limit, but reveals an extra space dimension, and an equivalence to M theory, in the limit of very strong coupling.
    We still don't know what the fundamental theory behind string theory is, but judging from all of these relationships, it must be a very interesting and rich theory, one where distance scales, coupling strengths and even the number of dimensions in spacetime are not fixed concepts but fluid entities that shift with our point of view.