Is a topological quantum field theory metrizable? Or else a TQFT coming from a subfactor?
For a given metric, are there always renormalization and Feynman diagrams?
Is there always a Feynman motive related to the theory?
Finally, does this Feynman motive depend on the choice of the metric?
My motivations come from the observation that the subfactors theory and the motives theory are both an "enriched Galois theory" so that I asked myself if there is a link between these two enrichment.
The path through TQFTs and Feynman motives could be a link.
All these questions could be unified by "Is the Feynman motive a topological invariant?".
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