QM Research Seminar: Braid Group Representations and Orbifoldization

Speaker: Jiahe Cai, University of Copenhagen

Abstract:

Let G be a finite group. By evaluation of a once-extended 3-2-1-dimensional G-equivariant topological field theory Z on the circle one obtains a G-ribbon category C. From a homotopy G-fixed point in this G-ribbon category C, we can construct two representations of framed braid groups fBn with n strands for any n ≥ 1: 1) We can construct a representation of fBn by evaluating Z on genus zero surfaces with G-bundle decoration. 2) We can orbifoldize the G-ribbon category C and obtain the fBn representation algebraically by using the braiding and twist of the orbifold category. We prove that these two representations are equivalent.