We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namely PSU(2)4k+ 2 for k = 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.
Publication Source (Journal or Book title)
Algebras and Representation Theory
Bruillard, P., Galindo, C., Ng, S., Plavnik, J., Rowell, E., & Wang, Z. (2020). Classification of Super-Modular Categories by Rank. Algebras and Representation Theory, 23 (3), 795-809. https://doi.org/10.1007/s10468-019-09873-9