Conformal nets IV: The 3-category

Author: 

Bartels, A
Douglas, C
Henriques, A

Publication Date: 

2018

Journal: 

ALGEBRAIC AND GEOMETRIC TOPOLOGY

Last Updated: 

2019-04-27T16:19:29.62+01:00

Issue: 

2

Volume: 

18

DOI: 

10.2140/agt.2018.18.897

page: 

897-956

abstract: 

© 2018, Mathematical Sciences Publishers. All rights reserved. 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.

Symplectic id: 

668627

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article