I am looking for resources (both pedagogical and newer research articles) on the connection between topological quantum computation and conformal field theory. In particular, a CFT description of anyonic braiding, fractional statistics, and/or the braid group of which assumes basic knowledge of conformal field theory and topological quantum computation. Does anyone know any good resources on this subject?
I would recommend Moore and Seiberg's "Lectures on RCFT" which is clear and beautiful. From their lectures, you can also get a sense of how the idea of modular tensor category goes into the subject.
In terms of a research article, I would recommend their paper "Classical and quantum conformal field theory".
Unfortunately, both references are sort of old since the developments are made in the 1980s.
A more modern paper on this subject that was written in the context of topological quantum computation would be the review article Non-Abelian Anyons and Topological Quantum Computation. It includes a review of conformal field theories in the appendix, a very gentle introduction to topological field theories in the beginning, and then dives into plenty of detail (at varying levels of gentleness).