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arXiv · 1705.05293

Classification of super-modular categories by rank

Paul Bruillard·César Galindo·Siu-Hung Ng·Julia Yael Plavnik·Eric C. Rowell·Zhenghan Wang
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Abstract

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.

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Paul Bruillard, César Galindo, Siu-Hung Ng, Julia Yael Plavnik, Eric C. Rowell, Zhenghan Wang. 2017-05-15. Classification of super-modular categories by rank. https://arxiv.org/abs/1705.05293

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