Abigail Watkins
Indiana University
Title
From the Category of Wilson Lines to G-equivariantization and Back Again
Abstract
Modular fusion categories have proven to be useful in studying many areas of math and mathematical physics such as link and manifold invariants, two-dimensional conformal field theory, and topological phases of matter. Recently, Ingo Runkel and Vincentas Mulevicius introduced a construction, the category of Wilson lines, which provides a way of building modular fusion categories from a collection of algebraic information called an orbifold datum. Another well-known way to produce examples of modular fusion categories is through the G-equivariantization of G-crossed ribbon categories whose neutral component is modular. Such categories give rise to a class of 'special' orbifold data in a natural way. In this talk, we will show that a category obtained from applying the Wilson lines construction to one of these special orbifold datum is equivalent as a braided ribbon category to the G-equivariantization of the category which the orbifold datum sits inside of.
