FQFT and cohomology
In the case that is a category of positive energy representation?s 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 .
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 TQFT from compact Lie groups – 3d Chern-Simons as a fully extended TQFT.
A standard textbook account is
(See the dedicated page Help me! I'm trying to understand Bakalov and Kirillov for help with understanding the computations in this book.)
and references cited there.