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Topological quantum field theory.
10
votes
Accepted
Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distingui...
I think this paper of Wakui says that the answer is "No". The Turaev-Viro invariants associated to the generalized $E6$ subfactors for $\mathbb{Z}/7$ don't seem to distinguish $L(7,1)$ and $L(7,2)$.
1
vote
Accepted
Does the following "symmetric" 2nd cohomology group of a finite group with coefficients in $...
I'm pretty sure now that $H^2_{sym} (\mathbb{Z}_4 \times \mathbb{Z}_2, \mathbb{Z}_2) = \mathbb{Z}_2 \times \mathbb{Z}_2$, so it can be nonzero. For comparison, in ordinary group cohomology $H^2 (\math …
7
votes
Accepted
Does the notion of a "coherent state" exist in TQFTs? (ETQFTs?)
Yes they do. In the geometric quantization approach to the 3d Chern-Simons TQFT, the vector space assigned to a closed surface is a space of holomorphic sections of a certain line bundle. In this cont …
10
votes
Interpreting the CS/WZW correspondence
One of the issues here is that if we define CS by its physics definition (action, fields) and similarly for WZW then it does seem like there is an equivalence. For example, on page 30 of
http://arxi …