Congruence Subgroups and Super-Modular Categories
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abstract
A super-modular category is a unitary pre-modular category with M"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary pre-modular category is the equivariantization of a either a modular or super-modular category. Physically, super-modular categories describe universal properties of quasiparticles in fermionic topological phases of matter. In general one does not have a representation of the modular group $mathrm{SL}(2,mathbb{Z})$ associated to a super-modular category, but it is possible to obtain a representation of the (index 3) $ heta$-subgroup: $Gamma_ heta
