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2018 Conformal nets IV: The $3$-category
Arthur Bartels, Christopher L Douglas, André Henriques
Algebr. Geom. Topol. 18(2): 897-956 (2018). DOI: 10.2140/agt.2018.18.897

Abstract

Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. We previously introduced a notion of composition, called fusion, between defects. We also described a notion of sectors between defects, modeling an interaction among or transformation between phase transitions, and defined fusion composition operations for sectors. In this paper we prove that altogether the collection of conformal nets, defects, sectors, and intertwiners, equipped with the fusion of defects and fusion of sectors, forms a symmetric monoidal 3 -category. This 3 -category encodes the algebraic structure of the possible interactions among conformal field theories.

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Arthur Bartels. Christopher L Douglas. André Henriques. "Conformal nets IV: The $3$-category." Algebr. Geom. Topol. 18 (2) 897 - 956, 2018. https://doi.org/10.2140/agt.2018.18.897

Information

Received: 4 January 2017; Revised: 28 June 2017; Accepted: 10 July 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859609
MathSciNet: MR3773743
Digital Object Identifier: 10.2140/agt.2018.18.897

Subjects:
Primary: 18D05, 81T05

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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