Conformal nets IV : The 3-category

Bartels, Arthur; Douglas, Christopher; Henriques, André

doi:10.2140/agt.2018.18.897

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Conformal nets IV: The $3$-category

Arthur Bartels, Christopher L Douglas and André Henriques

Algebraic & Geometric Topology 18 (2018) 897–956

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.

Keywords

conformal net, defect, sector, fusion, conformal field theory, topological field theory, von Neumann algebra, Connes fusion, $3$-category

Mathematical Subject Classification 2010

Primary: 18D05, 81T05

References

Publication

Received: 4 January 2017

Revised: 28 June 2017

Accepted: 10 July 2017

Published: 12 March 2018

Authors

Arthur Bartels
Mathematisches Institut Westfälische Wilhelms-Universität Münster Münster Germany

Christopher L Douglas
Mathematical Institute University of Oxford Oxford, United Kingdom

André Henriques
Mathematisch Instituut Universiteit Utrecht Utrecht, Netherlands

Volume 18, issue 2 (2018)