Boundaries, defects and Frobenius algebras

Abstract

The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new computational tools. The construction of CFT correlators based on combining tools from topological field theory and non-commutative algebra in tensor categories, which we summarize in this contribution, allows e.g. to discuss, apart from boundary conditions, also defect lines and disorder fields.

7 pages. Contribution to the 35th International Symposium Ahrenshoop on the Theory of Elementary Particles (Berlin, August 2002) and to the International Conference on Theoretical Physics (UNESCO, Paris, July 2002). For related proceedings contributions see http://tpe.physik.rwth-aachen.de/schweigert/proceedings.html