Theory Department
Conformal Field Theory and String Theory
Werner Nahm
Conformally invariant quantum field theories are exactly solvable in two
dimensions due to their infinite-dimensional symmetry group. Thus they
can be applied to many two-dimensional models near criticality.
In first place, we investigate applications of supersymmetric conformal
field theories in string theory.
On the world sheet of a string such a conformal theory is defined in a
natural way.
We take these theories to describe special, solvable string vacua and to
explore their moduli spaces, i.e. the deformations of these theories.
This makes it possible to probe geometrical objects arising in
compactifications of superstring theories, the so-called Calabi-Yau
manifolds.
Furthermore, we study conformal field theories on surfaces with
boundaries giving rise to new boundary states.
These can be used to describe non-perturbative objects in string theory,
so-called D-branes.
We are also interested in more general questions, namely the
classification of conformal field theories. The anomaly of the energy
momentum tensor, the so-called central charge c, is a first distinction.
For some interesting values of c we work on the classification of the
respective conformal theories. The mathematical methods include
algebraic geometry, differential geometry, Kac-Moody algebras and
modular forms.
Current projects
18. August 2000
www@th.physik.uni-bonn.de