57 research outputs found
On the Classification of Bulk and Boundary Conformal Field Theories
The classification of rational conformal field theories is reconsidered from
the standpoint of boundary conditions. Solving Cardy's equation expressing the
consistency condition on a cylinder is equivalent to finding integer valued
representations of the fusion algebra. A complete solution not only yields the
admissible boundary conditions but also gives valuable information on the bulk
properties.Comment: 7 pages, LaTeX; minor correction
Boundary Conditions in Rational Conformal Field Theories
We develop further the theory of Rational Conformal Field Theories (RCFTs) on
a cylinder with specified boundary conditions emphasizing the role of a triplet
of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that
solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is
equivalent to finding integer valued matrix representations of the Verlinde
algebra. These matrices allow us to naturally associate a graph to each
RCFT such that the conformal boundary conditions are labelled by the nodes of
. This approach is carried to completion for theories leading to
complete sets of conformal boundary conditions, their associated cylinder
partition functions and the -- classification. We also review the
current status for WZW theories. Finally, a systematic generalization
of the formalism of Cardy-Lewellen is developed to allow for multiplicities
arising from more general representations of the Verlinde algebra. We obtain
information on the bulk-boundary coefficients and reproduce the relevant
algebraic structures from the sewing constraints.Comment: 71 pages. Minor changes with respect to 2nd version. Recently
published in Nucl.Phys.B but mistakenly as 1st version. Will be republished
in Nucl.Phys.B as this (3rd) versio
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