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ISBN: 9781470435233

Publication Date: May 2019

Format: Paperback

Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect.
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Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index.

There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.
Pages 102
Dimensions 254 x 178
Date Published 30 May 2019
Publisher American Mathematical Society
Series Memoirs of the American Mathematical Society
Series Part Volume: 258 Number: 1237
Subject/s Calculus & mathematical analysis   Mathematical physics  
  • Acknowledgments
  • Introduction
  • Defects
  • Sectors
  • Properties of the composition of defects
  • A variant of horizontal fusion
  • Haag duality for composition of defects
  • The $1 \boxtimes 1$-isomorphism
  • Appendix A. Components for the 3-category of conformal nets
  • Appendix B. Von Neumann algebras
  • Appendix C. Conformal nets
  • Appendix D. Diagram of dependencies
  • Bibliography.
Arthur Bartels, Westfalische Wilhelms-Universitat Munster, Germany.

Christopher Douglas, University of Oxford, United Kingdom.

Andre Henriques, Universiteit Utrecht, The Netherlands.

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