String Theroy: the multi-dimensional universe
(from Cambridge University Quantum Gravity website)
In the standard model of particle physics, particles are considered as points moving through space, tracing out a line called the World Line. Unfortunately, there are a great number of different fundamental particles, which makes the construction of a unified theory difficult.
In String Theory, the myriad of particle types is replaced by a single fundamental loop, a `string'. As the string moves through time it traces out a tube, the World Sheet. The string is free to vibrate, and different vibrational modes on the string represent the different particle types. One mode of vibration, or `note', makes the string appear as an electron, another as a photon. There is even a mode describing the graviton, the particle carrying the force of gravity, which is an important reason why String Theory has received the attention it has. The original hope was that String Theory will be able to unify all of the known forces and particles together into a single `Theory of Everything'.
Extra dimensions
One of the most famous predictions of String Theory is that space-time has ten dimensions! At first sight, this may be seen as a reason to dismiss the theory altogether, as we obviously have only three dimensions of space and one of time. However, if we assume that six of these dimensions are curled up very tightly, then we may never be aware of their existence. Furthermore, having these so-called compact dimensions is very beneficial if String Theory is to describe a Theory of Everything. The idea that compact dimensions may lead to unifying theories is not new, but is actually over sixty years old, since the theory of Kaluza and Klein. In a sense, String Theory is the ultimate Kaluza-Klein theory.
For simplicity, it is usually assumed that the extra dimensions are wrapped up on six circles. For realistic results they aretreated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.
Cambridge University Quantum Gravity
W. Siegel, Introduction to String Field Theory (World Scientific, Singapore, 1988)
The Scecond Superstring Revolution
Topological Geometrodynamics: an attempt to unify fundamental interactions by assuming that physical spacetimes can be regarded as submanifolds of certain 8-dimensional space.