Logarithmic bulk and boundary conformal field theory and the full centre construction
Published in Conformal Field Theories and Tensor Categories, 2012
Reviews bulk and boundary conformal field theory in a form that includes logarithmic theories, defining the largest bulk theory compatible with a given boundary theory via the full centre of an algebra in a braided tensor category. This lets complicated bulk theories be built from simpler boundary ones, as illustrated by the central charge zero triplet model.
Abstract
We review the definition of bulk and boundary conformal field theory in a way suited for logarithmic conformal field theory. The notion of a maximal bulk theory which can be non-degenerately joined to a boundary theory is defined. The purpose of this construction is to obtain the more complicated bulk theories from simpler boundary theories. We then describe the algebraic counterpart of the maximal bulk theory, namely the so-called full centre of an algebra in an abelian braided monoidal category. Finally, we illustrate the previous discussion in the example of the W(2,3)-model with central charge 0.
Recommended citation: I. Runkel, M.R. Gaberdiel and S. Wood, Conformal Field Theories and Tensor Categories. Mathematical Lectures from Peking University, 93-168 (2014)
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