Is there any connection to CohFTs as defined by Witten in his 1988 paper (via topological twist) and the CohFTs as defined by Kontsevich and Manin (in the context of Gromov-Witten theory of course).

I mean, is there a general definition of CohFT such that every simple (physics or maths) example such as Donaldson theory, Vafa-Witten theory, Gromov-Witten theory, Donaldson-Thomas theory, etc falls under this definition?

  • $\begingroup$ Are you ok with factorisation algebras? You can translate everything to this language. $\endgroup$
    – user40276
    Aug 29, 2018 at 21:07
  • $\begingroup$ Can you please provide details? $\endgroup$
    – Gorbz
    Aug 30, 2018 at 7:26
  • $\begingroup$ I'm not the best person here to talk about factorisation algebras. For topological twists, you may want to look at arxiv.org/pdf/1805.10806.pdf . The point is that anything constructed from a BRST-BV like formalism will fit into this formalism too. But you want something less general I suppose. $\endgroup$
    – user40276
    Aug 31, 2018 at 20:33
  • $\begingroup$ Btw, I think that Witten defined Gromov-Witten cohomologically before Kontsevich-Manin in intlpress.com/site/pub/files/_fulltext/journals/sdg/1990/0001/… $\endgroup$
    – user40276
    Aug 31, 2018 at 20:38
  • $\begingroup$ Indeed, but unlike GW theory, Donaldson theory or Vafa-Witten theory do not fall under the same CohFT definition as the GW theory. Of course they live in different dimensions. But my question remains. Is there an umbrella definition for any CohFT for any dimension? $\endgroup$
    – Gorbz
    Aug 31, 2018 at 21:12


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