A Short Guide to Anyons and Modular Functors

Understand

To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems.

• A typical calculation using this theory will involve operations such as $\otimes$ to combine anyons, $F^{abc}_{d}$ to re-associate such combinations, and $R^{ab}_c$ to commute or braid these anyons.
• Although there is a powerful string-diagram notation that greatly assists these manipulations, we still appear to be operating on particles arranged on a one-dimensional line, algebraically ordered from left to right.
• The obvious question is, where is the other dimension? The topological framework for considering these anyons as truly living in a two dimensional space is known as a modular functor, or topological quantum field theory.