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I think the statement in Witten's paper, "Quantum Field Theory and the Jones Polynomial" saying the term is topological in the sense it is indeed independent of metric. However, he also mentioned, in order to make sense of this integration, i.e. make it to be a number, you need to choose a trivialization of tangent bundle, i.e. choose a framing. The tricky ...


This is a standard particle-vortex duality transformation. The idea is there exists a "dual" description of a superfluid, in which the bosons (to be precise, the Goldstone mode) is described by a 2-form(tensor) gauge field, and the vortices are now string-like "matter" charged under the gauge field. The effective action for phase fluctuations (i.e. Goldstone ...

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