String Theory

Originally, string theory was invented to describe the strong interactions in nuclear physics. This was superseded by QCD, the theory of quarks and gluons. However, the idea of replacing pointlike elementary particles by little thread, open or closed like rubber bands, proved extreme profitable in other circumstances: It was found that this theory automatically contains Einstein's theory of gravity while being a genuine quantum theory at the same time. Up to today, it is the only generally successful theory of quantum gravity.

Over the years, this theory turned out to be extremely rich and contains numerous internal connections as well as to other fields including mathematics. Studying strings one encounters extra dimensions, branes, supersymmetric field theories, black holes, and compactification geometries including noncommutative ones.

In many places, string theory generates connections between different types of theories: For example, gauge theories like the standard model of elementary particles have a dual description in terms of the geometry of a gravitational theory. In this case there are various interplays and one can use one description to obtain new information about the other theory.

It is expected that typical energy scales of string theory lay way beyond current experimental technology. However, with new experiments like LHC and hopefully the next linear collider coming up as well as cosmological observations providing a so far unknown amount of interesting data, string theorists are on the lookout for new interesting physics to come up that might give indications about the form of a final theory that string theory is currently our best candidate for.

In the meantime, there is still a lot to be understood about the structure of string theory and its implications for mathematics. In the past, the connection between mathematics and string theory has proved extremely fruitful and we expect it to continue to do so.

This is not the place to give a full account of the theory. A good starting point to learn more is the entry in wikipedia. At IUB, we taught an advanced undergraduate/graduate course on "Strings, Matrices and Branes" that partly followed the excellent text book by Zwiebach.