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Fusion of Defects.


Fusion of Defects

Arthur Bartels, Christopher L. Douglas, and Andre Henriques

American Mathematical Society


95 pages


Memoirs of the American Mathematical Society; Volume 258, Number 1237


Conformal nets provide a model for conformal field theories, say Bartels, Douglas, and Henriques, and they define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. Introducing an operation fusing defects, they prove that the fusion of two defects is again a defect, provided that the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodal) between two defects, and operations of the horizontal and vertical fusion of such sectors, and they say that their 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, then, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions, and the vertical fusion of two horizontal fusions of sectors. (Ringgold, Inc., Portland, OR)

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Article Type:Book review
Date:May 1, 2019
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