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Logarithmic Bulk and Boundary Conformal Field Theory and the Full Centre Construction

  • Ingo Runkel
  • Matthias R. Gaberdiel
  • Simon Wood
Part of the Mathematical Lectures from Peking University book series (MLPKU)

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.

Notes

Acknowledgements

This paper is based on talks given by IR at the conferences Conformal field theories and tensor categories (13–17 June 2011, Beijing) and Logarithmic CFT and representation theory (3–7 October 2011, Paris). IR thanks the Beijing International Center for Mathematical Research at Peking University and the Centre Emile Borel at the Institut Henri Poincare in Paris for hospitality during one month stays around these conferences. MRG and SW thank the Centre Emile Borel for hospitality during the second conference. The authors thank Alexei Davydov, Jürgen Fuchs, Azat Gainutdinov, Jérôme Germoni, Antun Milas, Victor Ostrik, Hubert Saleur, Christoph Schweigert, Alexei Semikhatov and Carl Stigner for helpful discussions. The research of MRG is supported in part by the Swiss National Science Foundation. IR is partially supported by the Collaborative Research Centre 676 ‘Particles, Strings and the Early Universe—the Structure of Matter and Space-Time’. SW is supported by the SNSF scholarship for prospective researchers and by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ingo Runkel
    • 1
  • Matthias R. Gaberdiel
    • 2
  • Simon Wood
    • 3
  1. 1.Fachbereich MathematikUniversität HamburgHamburgGermany
  2. 2.Institute for Theoretical PhysicsETH ZürichZürichSwitzerland
  3. 3.IPMUThe University of TokyoKashiwaJapan

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