Logarithmic bulk and boundary conformal field theory and the full centre construction

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.

71 pages, contribution to the proceedings of 'Conformal field theories and tensor categories' (Beijing, June 2011)

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• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• Representations of ${\bar{U}}_{q}s\ell (2|1)$ at even roots of unity
• Hopf and Frobenius algebras in conformal field theory