Functorial quantum field theory
The Reshetikhin-Turaev construction is the FQFT construction of a 3d TQFT from the data of a modular tensor category . It is something like the “square root” of the Turaev-Viro model on .
In the case that is a category of positive energy representations of a loop group of a Lie group , then this algebraically defined QFT is thought to be the result of quantization of Chern-Simons theory over the group .
As a boundary of the Crane-Yetter model
The Reshetikhin-Turaev model is a boundary field theory of the 4d TQFT Crane-Yetter model (Barrett&Garci-Islas&Martins 04, theorem 2) Related discussion is in Freed “4-3-2 8-7-6”.
Relation to Chern-Simons theory
The RT-construction for group is expected to be the FQFT of -Chern-Simons theory, though a fully explicit proof of this via quantization is currently not in the literature.
See at quantization of Chern-Simons theory for more on this.
Relation to conformal field theory
The Fuchs-Runkel-Schweigert-construction builds from the RT-construction explicitly the rational 2-dimensional 2d CFT boundary theory (see at holographic principle).
Original articles include
- Reshetikhin; Turaev, Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547–597. (pdf)
A standard textbook account is
- B. Bakalov & Alexandre Kirillov, Lectures on tensor categories and modular functors AMS, University Lecture Series, (2000) (web).
(See the dedicated page Help me! I'm trying to understand Bakalov and Kirillov for help with understanding the computations in this book.)
Discussion that relates the geometric quantization of -Chern-Simons theory to the Reshetikhin-Turaev construction of a 3d-TQFT from the modular tensor category induced by is in
and references cited there.
- Alain Bruguières, Alexis Virelizier, Hopf diagrams and quantum invariants, math.QA/0505119; Categorical centers and Reshetikhin-Turaev invariants, arxiv/0812.2426
The relation to the Crane-Yetter model was discussed in
Revised on December 27, 2015 17:36:31
by Manuel Bärenz?