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 This was superseded by QCD, the theory of quarks and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
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