Citation: Kirillov Jr, Alexander. "String-net model of Turaev-Viro invariants." arXiv preprint arXiv:1106.6033 (2011).
Web: https://arxiv.org/abs/1106.6033
Tags: Modular-tensor-categories, TQFTs,
This paper is a great folklore-buster, showing that the Turaev-Viro and Levin-Wen models are equivalent, in the sense that there is a canonical isomorphism between the ground states of the Levin-Wen model on an oriented surface and the vector space associated to that surface by the Turaev-Viro TQFT.
The fact that Turaev-Viro and Levin-Wen are equivalent is not much of a surprise. Special cases of this result have been established, sometimes only on the physical level of rigor, in
> Kadar, Zoltan, Annalisa Marzuoli, and Mario Rasetti. "Microscopic description of 2D topological phases, duality, and 3D state sums." Advances in Mathematical Physics 2010 (2010).
and
> Koenig, Robert, Greg Kuperberg, and Ben W. Reichardt. "Quantum computation with Turaev–Viro codes." Annals of Physics 325.12 (2010): 2707-2749.
This paper is very well done, especially in its treatment of boundaries.