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Product Code:  MEMO/258/1237 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 258; 2019; 100 ppMSC: 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. 
Table of Contents

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 3category of conformal nets

B. Von Neumann algebras

C. Conformal nets

D. Diagram of dependencies


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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.

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 3category of conformal nets

B. Von Neumann algebras

C. Conformal nets

D. Diagram of dependencies