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Conformal Field Theories and Tensor Categories

Proceedings of a Workshop Held at Beijing International Center for Mathematical Research

  • Conference proceedings
  • © 2014

Overview

Editors:
  1. Chengming Bai

    1. Chern Institute of Mathematics, Nankai University, Tianjin, People's Republic of China

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  2. Jürgen Fuchs

    1. Theoretical Physics, Karlstad University, Karlstad, Sweden

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  3. Yi-Zhi Huang

    1. Department of Mathematics, Department of Mathematics, Rutgers University, Piscataway, USA

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  4. Liang Kong

    1. Institute for Advanced Study, Tsinghua University, Beijing, People's Republic of China

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  5. Ingo Runkel

    1. Department of Mathematics, University of Hamburg, Hamburg, Germany

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  6. Christoph Schweigert

    1. Department of Mathematics, University of Hamburg, Hamburg, Germany

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  • First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications
  • Contributors include both mathematicians and physicists
  • Some long expository articles are especially suitable for beginners
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematical Lectures from Peking University (MLPKU)

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Table of contents (7 papers)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. From Hopf Algebras to Tensor Categories

    • N. Andruskiewitsch, I. Angiono, A. García Iglesias, B. Torrecillas, C. Vay
    Pages 1-31

  3. Pattern-of-Zeros Approach to Fractional Quantum Hall States and a Classification of Symmetric Polynomial of Infinite Variables

    • Xiao-Gang Wen, Zhenghan Wang
    Pages 33-65

  4. Virasoro Central Charges for Nichols Algebras

    • A. M. Semikhatov
    Pages 67-92

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

    • Ingo Runkel, Matthias R. Gaberdiel, Simon Wood
    Pages 93-168

  6. Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules

    • Yi-Zhi Huang, James Lepowsky, Lin Zhang
    Pages 169-248

  7. C 2-Cofinite \(\mathcal{W}\)-Algebras and Their Logarithmic Representations

    • Dražen Adamović, Antun Milas
    Pages 249-270

  8. C 1-Cofiniteness and Fusion Products for Vertex Operator Algebras

    • Masahiko Miyamoto
    Pages 271-279
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Keywords

About this book

The present volume is a collection of seven papers that are either
based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the
Beijing International Center for Mathematical Research, Peking University,  or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond
rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researcherslooking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Editors and Affiliations

  • Chern Institute of Mathematics, Nankai University, Tianjin, People's Republic of China

    Chengming Bai

  • Theoretical Physics, Karlstad University, Karlstad, Sweden

    Jürgen Fuchs

  • Department of Mathematics, Department of Mathematics, Rutgers University, Piscataway, USA

    Yi-Zhi Huang

  • Institute for Advanced Study, Tsinghua University, Beijing, People's Republic of China

    Liang Kong

  • Department of Mathematics, University of Hamburg, Hamburg, Germany

    Ingo Runkel, Christoph Schweigert

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