AnyonAtlas

Modular tensor categories

AnyonAtlas

A searchable database of modular and supermodular data, structural invariants, known realizations, and all possible condensation relations.

Full F- and R-symbols for categories of interest, with more to be added soon.

Browse the catalogExplore condensations

Exact data downloadable in preferred formats.

Explore the Database

Two complementary ways to work with the data

01 · CATALOG

Find and inspect individual data

Filter by numerical invariants, properties, realizations, fusion rings, subcategories, and symmetry groups.

02 · CONDENSATIONS

Trace the condensation structure

Browse graphs of Witt equivalence classes sorted by higher central charge.

Citation

Using data from this site

If the tools or data collected here are useful in your work, please cite The Anyon Atlas. When referring to a particular category, include its record ID so that the entry can be identified unambiguously.

BibTeX
@misc{berean-dutcher2026anyonatlas,
  author = {Berean-Dutcher, Jonah and C{\'o}rdova, Clay and Parra-Martinez, Julio and Tuddenham, Richard},
  title  = {The Anyon Atlas},
  year   = {2026}
}

Corrections and requests

Found an error or have an improvement?

If you identify any errors in the data or would like a feature to be added, please reach out to rtuddenh@uchicago.edu. Please let us know if you find information presented here to be out of date.