Fusion of defects
著者
書誌事項
Fusion of defects
（Memoirs of the American Mathematical Society, no.1237）
American Mathematical Society, 2019
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注記
Includes bibliographical references
"March 2019, volume 258, number 1237 (first of 7 numbers) "
内容説明・目次
内容説明
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.
目次
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.
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