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In Campos-Willwacher 16 and followups, the authors highlight that the quasi-iso from the graph complex to the de Rham complex of configuration spaces sends edges to AKSZ-model Feynman propagators, hence that those differential forms “$g_{i j}$” pulled back from the boundary spheres of the FM-compactification are essentially to be identified with the Feynman propagators of some (any?) AKSZ sigma-model.
This sounds quite plausible, but has this been made precise? Campos-Willwacher seem to indicate that the details for this claim are implicit in articles by Alberto Cattaneo and coauthors. This sounds also rather plausible!
But where exactly? Where in the literature would this claim have been substantiated, that the quasi-iso from graph complexes to de Rham complexes of configuration spaces sends edges to AKSZ Feynman propagators?
(I have emailed Alberto about it. But if anyone has any insight otherwise, let me know.)
ah, probably this here:
Remark 3.6 in
re-amplified as remark 11 in
and these two references really mainly recall the observation of Section 2 of
I am collecting these pointers here at Fulton-MacPherson operad, for the moment, but this should eventually get its own discussion somewhere…
Added a reference:
The following paper constructs a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable for being rational (and indeed definable integrally) in de Rham cohomology:
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