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Fusion of Defects

Arthur Bartels Westfälische Wilhelms-Universität Münster, Münster, Germany
Christopher Douglas University of Oxford, Oxford, United Kingdom
André Henriques Universiteit Utrecht, Utrecht, The Netherlands
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Softcover ISBN: 978-1-4704-3523-3
Product Code: MEMO/258/1237
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AMS Member Price: $48.60 Electronic ISBN: 978-1-4704-5065-6 Product Code: MEMO/258/1237.E List Price:$81.00
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AMS Member Price: $72.90 Click above image for expanded view Fusion of Defects Arthur Bartels Westfälische Wilhelms-Universität Münster, Münster, Germany Christopher Douglas University of Oxford, Oxford, United Kingdom André Henriques Universiteit Utrecht, Utrecht, The Netherlands Available Formats:  Softcover ISBN: 978-1-4704-3523-3 Product Code: MEMO/258/1237  List Price:$81.00 MAA Member Price: $72.90 AMS Member Price:$48.60
 Electronic ISBN: 978-1-4704-5065-6 Product Code: MEMO/258/1237.E
 List Price: $81.00 MAA Member Price:$72.90 AMS Member Price: $48.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$121.50 MAA Member Price: $109.35 AMS Member Price:$72.90
• Book Details

Memoirs of the American Mathematical Society
Volume: 2582019; 100 pp
MSC: Primary 81; 46;

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.

• Chapters
• Acknowledgments
• Introduction
• 1. Defects
• 2. Sectors
• 3. Properties of the composition of defects
• 4. A variant of horizontal fusion
• 5. Haag duality for composition of defects
• 6. The $1 \boxtimes 1$-isomorphism
• A. Components for the 3-category of conformal nets
• B. Von Neumann algebras
• C. Conformal nets
• D. Diagram of dependencies

• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 2582019; 100 pp
MSC: Primary 81; 46;

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.

• Chapters
• Acknowledgments
• Introduction
• 1. Defects
• 2. Sectors
• 3. Properties of the composition of defects
• 4. A variant of horizontal fusion
• 5. Haag duality for composition of defects
• 6. The $1 \boxtimes 1$-isomorphism
• A. Components for the 3-category of conformal nets
• B. Von Neumann algebras
• C. Conformal nets
• D. Diagram of dependencies
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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