Classification of Metaplectic Fusion Categories

Understand

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for $so(2p+1)_2$.

• These categories describe non-abelian anyons dubbed `metaplectic anyons'.
• We obtain explicit expressions for all the $F$- and $R$-symbols.
• Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.