Classification of Metaplectic Fusion Categories

TL;DR

This paper classifies a family of fusion categories related to metaplectic anyons, providing explicit formulas for their structural symbols and analyzing their equivalence classes based on gauge invariants.

Contribution

It offers the first explicit expressions for all F- and R-symbols of these categories and proposes a classification scheme for their monoidal equivalence classes.

Findings

Explicit F- and R-symbols derived for the categories.

A conjectured classification scheme for monoidal equivalence classes.

A function quantifying the number of equivalence classes.

Abstract

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.