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I'm reading this (review?) article https://www.sciencedirect.com/science/article/pii/0370157391901175 on topological field theories.

In section 3.2 (page 142) they seem to be claiming that for any theory with global SUSY there is a "nicolai map" which allows you to reexpress the partion function as that corresponding to a free boson. Am I misunderstanding this? Is global SUSY such a strong restriction that everything just ends up being equally well expressed as a free boson? If so, how are theories with SUSY any interesting if they're all free bosons.

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  • $\begingroup$ Maybe this mean that some SUSY theories is topological? Few years ago people study partition function for different SUSY theories using supersymmetric location, and partition function localized on fixed point, where you need calculate only determinant for free theory. $\endgroup$
    – Nikita
    Commented Jan 4, 2020 at 9:52

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