Representations of the loop braid groups from braided tensor categories

The loop braid group is the motion group of unknotted oriented circles in R3. 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 R3 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.