Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple current is half-integral and k is odd.Comment: Added reference, minor change

D-brane conformal field theory

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism \omega of the fusion rules that preserves conformal weights. Non-trivial automorphisms \omega correspond to D-brane configurations for arbitrary conformal field theories.Comment: 7 pages, LaTeX2e. Slightly extended version of a talk given by J. Fuchs at the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, September 199

Conformal field theory, boundary conditions and applications to string theory

This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.Comment: 45 pages, LaTeX2

The action of outer automorphisms on bundles of chiral blocks

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik-Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bundle of chiral blocks is typically a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented; the proposed relation generalizes the Verlinde formula. Our results have applications to conformal field theories based on non-simply connected groups and to the classification of boundary conditions in such theories.Comment: 46 pages, LaTeX2e. Final version (Commun.Math.Phys., in press). We have implemented the fact that the group of automorphisms in general acts only projectively on the chiral blocks and corrected some typo