Timeline for Difference between TCFTs and 2D TQFTs
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7, 2020 at 19:40 | history | bounty ended | Markus Zetto | ||
| May 6, 2020 at 9:30 | vote | accept | Markus Zetto | ||
| May 5, 2020 at 19:03 | comment | added | user1504 | You might be better off reading Costello's paper Topological Conformal Field Theories and Calabi-Yau algebras. Lurie's is more generality than needed for this. | |
| May 5, 2020 at 19:01 | comment | added | user1504 | No, it's not because of any integration. In his cobordism paper, Lurie only describes the B-model as a TQFT (example 1.4.1). He doesn't say what the category assigned to a point is, and without that info, I don't believe you can construct a chain-level theory. In Lurie's world, the dependence on families of complex structures sneaks in through the cobordism hypothesis. Having a fully dualizable object gives you something that's acted on naturally by families of bordisms of circles, and such bordisms are Riemann surfaces, with all their classical connection to the moduli of curves. | |
| May 5, 2020 at 17:27 | comment | added | Markus Zetto | Thank you for the answer! Especially the last part was very helpful. Could you explain a bit more about the metric dependence of the TCFTs, it seems to me that (even though as you state this is only through a certain homology class, I don't really understand how this class is defined) this would make the field theory not topologic? I am asking this because e.g. Lurie gave a description of the closed-string B-model in a completely axiomatic way (as a monoidal functor) in his paper on TFTs, without mentioning anything about a worldsheet metric, is this because we integrate over it? Greetings, | |
| May 5, 2020 at 16:56 | history | answered | user1504 | CC BY-SA 4.0 |