nLab
Turaev-Viro model

Idea

The Turaev-Viro model is a 3-dimensional topological quantum field theory construction induced from a modular tensor category. It is something like the “norm square” of the Reshetikhin-Turaev construction on $𝒞$.

References

The original article is

• V. G. Turaev and O. Ya. Viro, State sum invariants of 3-manifolds and quantum 6jsymbols, Topology 31 (1992), no. 4, 865–902, DOI 10.1016/0040-9383(92)90015-A. MR1191386 (94d:57044

• John Barrett, Bruce Westbury, Invariants of piecewise-linear 3-manifolds, Trans. Amer. Math. Soc. 348 (1996), no. 10, 3997–4022, DOI 10.1090/S0002-9947- 96-01660-1. MR1357878 (97f:57017)

Refinement of the construction to an extended TQFT is in

• Alexander Kirillov Jr., Benjamin Balsam, Turaev-Viro invariants as an extended TQFT

Discussion that relates the geometric quantization of $G$-Chern-Simons theory to the Reshetikhin-Turaev construction of a 3d-TQFT from the modular tensor category induced by $G$ is in

• Jørgen Andersen, A geometric formula for the Witten-Reshetikhin-Turaev Quantum Invariants and some applications (arXiv:1206.2785)

and references cited there.

A relation to the Levin-Wen model is discussed in

• Alexander Kirillov Jr, String-net model of Turaev-Viro invariants (arXiv:1106.6033)