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Citation: Burton, Simon. "A short guide to anyons and modular functors." arXiv preprint arXiv:1610.05384 (2016).
Tags: Expository, Pedagogical, To-read
This short expository article does exactly what it says it will: it details the theory of anyons and modular functors. The thesis is that the theory of MTCs is amazing and compact, and takes the two-dimensional theory of anyons and "compresses" it into 1 dimension. TQFTs and modular functors are the full 2-dimensional picture that is getting compressed. This article makes the connection clear, and shows plenty of pretty pictures along the way.
The TQFT axioms are layed out really well, and this is arguably the best place to learn about them. The hexagon and pentagon axioms are given beautiful little diagrams. Simon claims his target audience to be "working physicists", but this exposition seems suited to mathematicians as well.