34,257 research outputs found
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
Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory
The correlation functions of a two-dimensional rational conformal field
theory, for an arbitrary number of bulk and boundary fields and arbitrary world
sheets can be expressed in terms of Wilson graphs in appropriate
three-manifolds. We present a systematic approach to boundary conditions that
break bulk symmetries. It is based on the construction, by `alpha-induction',
of a fusion ring for the boundary fields. Its structure constants are the
annulus coefficients and its 6j-symbols give the OPE of boundary fields.
Symmetry breaking boundary conditions correspond to solitonic sectors.Comment: 9 pages, LaTeX2e. Invited talk by Christoph Schweigert at the TMR
conference ``Non-perturbative quantum effects 2000'', Paris, September 200
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
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