UC Santa Barbara

Phase transitions can be understood through the formation of Bose condensates. Anyon condensation is similarly an important tool for transitioning between systems modeled by modular tensor categories. The condensation process can be understood as a functor from one modular tensor category to another fusion category with a modular subcategory.

This dissertation focuses on understanding the condensation functor. After reviewing modular tensor categories, we present and comment on the relationship between two descriptions of the resulting category. We then present general results on the modular data of the resulting category and demonstrate how to explicitly compute the new $F$- and $R$-symbols. We finish off with some applications of our work and some speculations about where they might go from here.

Chapter 4 is devoted to implementing the functorial definition of condensation so that it can be carried out by a computer, and a full Mathematica implementation is provided in Supplemental A: Mathematica Code. Supplemental B: $(G_2)_3$ Data provides categorical data for the modular tensor category $(G_2)_3$, which is not otherwise widely available.