/sci/ - Science & Math

Since we were on the topic anyway:
>what are you studying?
Studying WZW theories through TQFT via the Witten invariant.
>any cool problems?
See thread.
>any cool theorems or remarks?
You can actually construct a projective representation of the Artin group with the monodromy of the Knizhnik-Zomolodchikov equations for the conformal blocks of a CFT. Coupled with the Verlinde-Seiberg formula being equivalent to the operator algebra hypothesis of a CFT this shows that there is a deep connection between braid group representations (which is a geometric property) and TQFTs on links (which is a topological property) through CFTs. This echoes the principal bundle-holonomy equivalence that I have mentioned a few months ago and may serve as precisely the bridge between topology and geometry that I need in order to characterize AdS/CFT.
Probably not though lmfoa.
>reference suggestions?
Turaev, Kohno.
>???
That's an open problem.
>>8957834
>but that cobordisms won't behave the way you want to under a TQFT (which I assume is what actually interests you).
So you're saying that there probably won't exist any [math]\sigma[/math] that satisfies both cobordism properties and entropy properties? Why do you think that would be the case?
Also I don't think there's anything stopping me from assuming such a [math]\sigma[/math] exists and work until I hit a wall (or not), which is basically what I meant in >>8957001.