Timeline for Two vague questions about TFT
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2022 at 22:23 | comment | added | Ed Segal | @DavidBen-Zvi Thanks for the link! I don't understand much of Pavel's answer to that other question but it looks like the kind of thing I wanted. I'll ask Dario... | |
| Mar 28, 2022 at 17:52 | comment | added | David Ben-Zvi | Second, one POV on the field theory you're asking about (generated by HH^*(X)) is that it's a (or the) {\it theory of observables} for the B-model. In general any TFT is canonically defined relative to a (truncated) TFT of one dimension higher defined using observables (in your case, local operators). The former we think of as describing states, the latter expresses observables (eg as captured in the Costello-Gwilliam formalism by evaluating factorization homology of a factorization algebra). | |
| Mar 28, 2022 at 17:48 | comment | added | David Ben-Zvi | @EdSegal Two comments of things I learned from Pavel: First as to E_2 modules over HH^*, it's close but not D(X) in general, see Pavel's answer here: mathoverflow.net/questions/371637/… | |
| Mar 28, 2022 at 16:15 | comment | added | Pavel Safronov | @EdSegal: the 2-category $\mathrm{HH}^\bullet(X)\mathrm{-mod}\mathrm{-mod}$ is extensively studied by Dario Beraldo in relation to singular support of coherent sheaves. If $X$ is smooth, then $\mathrm{HH}^\bullet(X)\mathrm{-mod}\mathrm{-mod}$ is equivalent to $\mathrm{ShvCat}(X_{dR})$, the 2-category of crystals of categories over $X$. I don't know a good name for the corresponding 3d TQFT. | |
| Mar 28, 2022 at 15:42 | comment | added | Pavel Safronov | @skd: the only explanation I have is that people have computed twists of nonlinear gauged sigma-models and the higher-dimensional Chern--Simons/RW theories do not arise. It might be possible that they arise from twisting some higher spin theories, but I know much less about them. | |
| Mar 28, 2022 at 13:53 | comment | added | Ed Segal | That is a pretty comprehensive answer to part 1. For part 2, I wouldn't be surprised if E_2 modules (properly understood) over HH(X) are equivalent to D(X), and maybe that's all that happens. But I'm kind of guessing here. | |
| Mar 28, 2022 at 13:52 | comment | added | Ed Segal | Fantastic thanks Pavel! I wasn't sure if anyone was still looking at MO... | |
| Mar 28, 2022 at 13:42 | comment | added | skd | How do you show that the higher-dimensional Chern-Simons theories don't arise from topological twisting? (Or, more generally, why do the odd-dimensional TQFTs associated to symplectic manifolds not arise as topological twists?) | |
| Mar 28, 2022 at 11:33 | history | answered | Pavel Safronov | CC BY-SA 4.0 |