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I have come across topological twists on numerous occasions but I have never actually seen them explained in an understandable way. So, I was wondering

  • What does it physically mean to topologically twist a theory?
  • What does it mathematically mean to topologically twist a theory?
  • What is the motivation for talking about topological twists?
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So, I think I've found an answer to my own question. One can take a supersymmetric theory defined on $\mathbb{R}^n$ and topologically twist it by redefining the rotation group of the theory into a mixture of the (spacetime) rotation group and the R-symmetry group.

Physically, this is just making one sector of the theory "more apparent". We can then restrict to this sector of the theory to get a topological field theory. In general, we will lose the supersymmetry (or at least lose some of it) since we are only considering one sector of the theory.

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  • $\begingroup$ Could you possibly give any reference for self studying these ? $\endgroup$
    – Vlatko
    Dec 30, 2020 at 15:38
  • $\begingroup$ @chaveroche I have found these lecture notes arxiv.org/abs/hep-th/0504147 quite pedagogical, although I am a bit of a novice myself, so there might be better references that I am unaware of. $\endgroup$
    – arow257
    Jan 12, 2021 at 21:32

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