String theory is one of the most exciting and profound developments in modern theoretical physics. Unfortunately it is a highly technical subject that can only be well understood using the tools of Quantum Field Theory. It also doesn’t hurt to know some mathematics like Group Theory, Differential Geometry, and Algebraic Geometry. Needless to say this is prohibitive for most people who are far too busy doing other things. String theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near 10 to the 33 centimeter, or about a millionth of a billionth of a billionth of a centimeter.
This means that strings are far to small to see by the current technology and so string theorists must devise clever methods to test the theory than just looking for little strings in particle experiments. String theory is a science in progress; we are still learning new and unexpected things about it everyday. Whether or not string theory actually describes the universe that we live in is not known – yet. As we will see it has remarkable potential to do so. Superstrings live in a 10-dimensional spacetime, but we observe a 4-dimensional spacetime.
Somehow we need to link the two if superstrings are to describe our universe. To do this we curl up the extra 6 dimensions into a small compact space. This is actually a very old idea dating back to the 1920’s and the work of Kaluza and Klein. This is often called Kaluza-Klein theory. The idea that our universe might have more than the three familiar spatial dimensions is one which was introduced more than half a century before the advent of string theory. The basic premise of such theories is that a dimension can be either large and directly observable or small and essentially invisible.
The five superstring theories appear to be very different when viewed in terms of their descriptions in weakly coupled perturbation theory. In fact the major revelation of the past few years is the fact that they are all related to each other by various string dualities. We say two theories are dual when they both describe the same physics. The dualities between the various string theories provide strong evidence that they are simply different descriptions of the same underlying theory.
Each description has its own regime of validity, and in certain limits another description takes over just when the original one is breaks down. So given this new phase 11-dimensional phase of string theory, and the various dualities between string theories, we’re led to the very exciting prospect that there is only a single fundamental underlying theory — M-theory. This uniqueness is very appealing, and much of the work in this field will be directed toward formulating the full quantum M-theory The classical description of gravity known as General Relativity, contains solutions which are called “black holes”.
There are many different kinds of black hole solutions but they share some common characteristics. The event horizon is a surface in spacetime which, loosely speaking, divides the inside of the black hole from the outside. The gravitational attraction of a black hole is so strong that any object that crosses the event horizon, including light, can never escape out of the black hole. Classical black holes are therefore relatively featureless, but they can be described by a set of observable parameters such as mass, charge, and angular momentum.
Black holes turn out to be important “laboratories” in which to test string theory, because the effects of quantum gravity turn out to be important even for large macroscopic holes. Black holes aren’t really “black” since they radiate. Since string theory is, among other things, a theory of quantum gravity, it should be able to describe black holes in a consistent way. In fact there are black hole solutions which satisfy the string equations of motion. Superstring theories also have some special black hole solutions which are themselves supersymmetric, in that they preserve some supersymmetry.
Superstring theory is a very exciting area of study because it has the serious potential to be the right theory for describing the fundamental nature of our universe. All the elements are in there: quantum physics, bosons, fermions, gauge groups, and gravity. In the last several years there has been great progress in understanding the overall structure of the theory including D-branes and string duality. String theory has been applied with great success to the study of black hole physics and quantum gravity. However, there is much work yet to be done.