I don't think there are any Witten-type TQFTs which are directly relevant to condensed matter physics. Witten-type TQFTs are very strange beasts: they violate spin-statistics, they aren't unitary, etc. It'd be pretty tricky to find a physical system you could model with one in the usual way.

There are some indirect connections between Chern-Simons theory and Gromov-Witten theory, but that's all I can think of.

This post imported from StackExchange Physics at 2014-04-05 04:33 (UCT), posted by SE-user user1504