The Anyon Atlas
Abstract
We classify possible topological quantum field theories in 2+1 dimensions with up to 22 anyons in the bosonic case and up to 26 in the fermionic case, through the modular data of modular and supermodular tensor categories. We construct such data via congruence representations of SL(2,ℤ) using a numerical optimization algorithm that scales to high rank. We chart the relations between the resulting theories, including anyon condensations and Chern-Simons realizations. We find examples of modular data that do not appear to arise from any Chern-Simons theory by any sequence of condensations of anyons or gaugings of ordinary global symmetries. These examples give qualitatively new topological quantum field theories, which go beyond any notion of gauge theory. For examples in this class with 11 and 12 anyon types, we solve the pentagon and hexagon equations explicitly, showing that these modular data are realized by full unitary topological quantum field theories. We also introduce https://www.AnyonAtlas.org, an online resource for exploring the data.
Related
- Anyon Proliferation and Anyon Superconductivity in Higgsing Transitions via Conformal Embeddings
- A nonabelian anyon violates Haag duality
- Exchange and Exclusion in the Non-abelian Anyon Gas
- Topological cosets via anyon condensation and applications to gapped QCD2
- Non-invertible anyon condensation and level-rank dualities
BibTeX
@misc{bereandutcher2026anyon,
title = {{The Anyon Atlas}},
author = {Jonah Berean-Dutcher and Clay Cordova and Julio Parra-Martinez and Richard Tuddenham},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25439},
eprint = {2610.25439},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25439},
}
RIS
TY - UNPB
TI - The Anyon Atlas
AU - Jonah Berean-Dutcher
AU - Clay Cordova
AU - Julio Parra-Martinez
AU - Richard Tuddenham
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25439
UR - https://arxiv.org/abs/2610.25439
AB - We classify possible topological quantum field theories in 2+1 dimensions with up to 22 anyons in the bosonic case and up to 26 in the fermionic case, through the modular data of modular and supermodular tensor categories. We construct such data via congruence representations of SL(2,ℤ) using a numerical optimization algorithm that scales to high rank. We chart the relations between the resulting theories, including anyon condensations and Chern-Simons realizations. We find examples of modular data that do not appear to arise from any Chern-Simons theory by any sequence of condensations of anyons or gaugings of ordinary global symmetries. These examples give qualitatively new topological quantum field theories, which go beyond any notion of gauge theory. For examples in this class with 11 and 12 anyon types, we solve the pentagon and hexagon equations explicitly, showing that these modular data are realized by full unitary topological quantum field theories. We also introduce https://www.AnyonAtlas.org, an online resource for exploring the data.
ER -