Conformal nets V: dualizability
Algebraic Topology
2019-05-10 v1 Mathematical Physics
Category Theory
math.MP
Operator Algebras
Abstract
We prove that finite-index conformal nets are fully dualizable objects in the 3-category of conformal nets. Therefore, assuming the cobordism hypothesis applies, there exists a local framed topological field theory whose value on the point is any finite-index conformal net. Along the way, we prove a Peter-Weyl theorem for defects between conformal nets, namely that the annular sector of a finite defect is the sum of every sector tensor its dual.
Cite
@article{arxiv.1905.03393,
title = {Conformal nets V: dualizability},
author = {Arthur Bartels and Christopher L. Douglas and André Henriques},
journal= {arXiv preprint arXiv:1905.03393},
year = {2019}
}