Geodesic
Conformal nets IV : The 3-category
Bartels, Arthur1 ; Douglas, Christopher2 ; Henriques, André3
1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Münster, Germany
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom
3 Mathematisch Instituut, Universiteit Utrecht, Utrecht, Netherlands
Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 897-956

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2018.18.897
Classification : 18D05, 81T05
Keywords: conformal net, defect, sector, fusion, conformal field theory, topological field theory, von Neumann algebra, Connes fusion, $3$-category

Bartels, Arthur 1 ; Douglas, Christopher 2 ; Henriques, André 3

1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Münster, Germany
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom
3 Mathematisch Instituut, Universiteit Utrecht, Utrecht, Netherlands 
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Bartels, Arthur; Douglas, Christopher; Henriques, André. Conformal nets IV : The 3-category. Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 897-956. doi: 10.2140/agt.2018.18.897

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