Integral Metaplectic Modular Categories

Abstract

A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these categories are group theoretical. For the special case of integral categories $\mathcal{C}$ with the fusion rules of $SO(8)_2$ we determine the finite group $G$ for which $Rep(D^{\omega}G)$ is braided equivalent to $\mathcal{Z}(\mathcal{C})$. In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point.