PreprintCC BY-SA 4.0arXiv
Superselection theory for 2D braided quantum spin systems via Connes fusion
Abstract
The article arXiv:2410.21454 constructed a braided W*-tensor category of superselection sectors associated to a net of von Neumann algebras on a suitably geometric poset using localized and transportable endomorphisms. In this article, we construct an equivalent tensor product and braiding using the Connes fusion tensor product without localizing, using ideas from arXiv:1812.04470 for conformal nets. As an application, we prove that the category of superselection sectors associated to the 2D braided quantum spin system constructed from a unitary braided fusion category ℬ in arXiv:2506.19969 is equivalent to Hilb(ℬ)op, the opposite of the unitary ind-completion of ℬ, as a braided W*-tensor category.
Related
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BibTeX
@misc{faurot2026superselection,
title = {{Superselection theory for 2D braided quantum spin systems via Connes fusion}},
author = {Gregory Faurot and Charlton Li and David Penneys and Emeline Sherman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20725},
eprint = {2609.20725},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20725},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Superselection theory for 2D braided quantum spin systems via Connes fusion
AU - Gregory Faurot
AU - Charlton Li
AU - David Penneys
AU - Emeline Sherman
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20725
UR - https://arxiv.org/abs/2609.20725
AB - The article arXiv:2410.21454 constructed a braided W^*-tensor category of superselection sectors associated to a net of von Neumann algebras on a suitably geometric poset using localized and transportable endomorphisms. In this article, we construct an equivalent tensor product and braiding using the Connes fusion tensor product without localizing, using ideas from arXiv:1812.04470 for conformal nets. As an application, we prove that the category of superselection sectors associated to the 2D braided quantum spin system constructed from a unitary braided fusion category ℬ in arXiv:2506.19969 is equivalent to Hilb(ℬ)^op, the opposite of the unitary ind-completion of ℬ, as a braided W^*-tensor category.
ER -