I posted this question to physics.SE last week (cf. here), but it got not attention. I hope it is not too trivial to post it here.
According to ref.1, the correlation functions of a Chern-Simons theory are topological invariants, up to the so-called framing, that is, the trivialisation of $TM\oplus TM$. The origin of this framing dependence is the UV divergences, which require a regularisation. The standard choice is to use point-splitting, where links are fattened up.
How exactly does framing the link introduce a dependence on the trivialisation of $TM\oplus TM$? What role does this bundle play here?
How can an observable possibly depend on a trivialisation? To me, that's like saying that, for example, the temperature of a black hole depends on the system of coordinates you use. Nonsense!
- Chern-Simons Theory and Topological Strings, M. Mariño, arXiv:hep-th/0406005.