The attempt to unite the four forces of Nature - electromagnetism, gravity, the strong nuclear force and the weak nuclear force - requires ten dimensions In terms of superstring theory, this means that superstrings can only vibrate in 10 dimensions. Each particle is described as a resonance of a superstring.

In ten dimensions, there is just enough room to include Einstein's equations and quantum mechanics. Quantum strings have a finite size. The Heisenberg uncertainty principle suggests that they are about 10 ^-34 cm. They can acquire angular mmommentum even if they lack mass. Due to quantum fluctautions, a string can acquire up to 2h (h = Planck's constant) of angular momentum without gaining mass. This is in agreement with the properties of the carriers of all known fundamental forces, such as the photon and the graviton.

Before the Big Bang the universe was ten-dimensional. However it was unstable and broke up into a four-dimensional universe and a six-dimensional universe. The six-dimensional universe curled up into Planck length, a size too small to see or probe.

Although superstring theory seems overwhelming in beauty, it's mathematics is difficult and not yet solved out. It is the inherent quantum strings that demand the existence of higher dimensions.

Superstring theory is based on supersymmetry, the symmetry that can exchange half-integer spin particles with integral spin particles.

There are super theories in 11 dimensions based on membranes as well as point particles - called supergravity. Point particles are called 0-branes, strings are 1-branes, membranes are 2-branes and so on. Since, in p-dimensional cases we get p-branes, the membranes are sometimes called pea brains.

This is another aspect of superstring theory and goes by the name M-theory. This theory unites 5 superstrings into one theory including the p-branes.

In 1984, Kikkawa and Yamasaki showed curling up an extra dimension into a circle of R radius was the same as curling up the dimension with 1/R radius. Because it represents a duality, it is known as T-duality. When applied to superstrings, we can reduce 5 of the various string theories into 3. However, T-duality is a perturbative duality, meaning that it needs perturbation theory as a tool.

However, for years it was thought that T-duality only applied to closed strings. But in 1995, Joseph Polchinski realized that T-duality applied to open stirngs as well, provided that the change between large and small radii was accompanied by a change in conditions at the end points of the string.

Later, physicists were able to find duality between perturbative and non-perturbative regions of string theory - S duality. Paul Townsend and Edward Witten showed that there was a duality between a 10-dimensional type of strings and 11-dimensional supergravity. In this manner, the non-perturbative region of this type of strings, that was formerly a forbidden region, was actually governed by 11-dimensional supergravity theory, with one dimension curled up.

Read more:
Superstring theory in Wikipedia
Official string theory web site