Representations of the loop braid groups from braided tensor categories

Abstract

The loop braid group is the motion group of unknotted oriented circles in ${\mathbb{R}}^3$. In this paper, we study their representations through the approach inspired by two dimensional topological phases of matter. In principle, the motion of loops in ${\mathbb{R}}^3$ reduces to the motions of points in a two dimensional sliced plane. We realize this physical picture in terms of braided tensor categories and their braid group representations.

9 pages

References in corpus (1)

• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory