Classification of super-modular categories

Abstract

We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank $8$. In particular we find three distinct families of prime categories in rank $8$ in contrast to the lower rank cases for which there is only one such family.

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Fermionic Modular Categories and the 16-fold Way
• A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
• Congruence Subgroups and Generalized Frobenius-Schur Indicators
• Classification of Rank 5 Premodular Categories
• Rank 4 Premodular Categories
• Classification of Rank 6 Modular Categories with Galois Group $⟨(012)(345)⟩$
• On slightly degenerate fusion categories
• A complete classification of unitary fusion categories tensor generated by an object of dimension $\frac{1+\sqrt{5}}{2}$

Cited by in corpus (2)

• Modular categories with transitive Galois actions
• Pre-modular fusion categories of small global dimensions