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In 2D (time + space) there is no notion of statistic. So particles can be described in terms of bosonic and fermionic fields.

Well-known example is Thirring/Sine-Gordon duality. There are also some examples: $\phi^4$ theory kinks as fermions?

  1. Are some examples of application of bosonization in supersymmetry?

  2. Is it possible to describe some SUSY theory only in terms of bosonic fields?

  3. What is then meaning of SUSY transformations, realized in terms of bosons?

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    $\begingroup$ Tricky question. If you are pining for a SUSY theory whose bosons are Fermionized to yield a clean fermionic theory, tough luck. However, there is a tandem mutation of fermions and bosons, symphysis, under nonabelian duality transformations, Canonical non-Abelian dual transformations in supersymmetric field theories, T Curtright & C Zachos, 1995, PhysRev D52 R573(R) ... $\endgroup$ Jul 9 '20 at 13:22
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    $\begingroup$ ...which maps Noether currents to topological/nonlocal currents, as in bosonization. $\endgroup$ Jul 9 '20 at 13:22
  • $\begingroup$ @CosmasZachos, thank you! But unfortunately I don't understand how your comment related to my question.. Is some known examples of such fermionic description of SUSY theory? $\endgroup$
    – Nikita
    Jul 9 '20 at 16:01
  • $\begingroup$ As I said, I don't know of an explicit one. But bosonization is a duality, and there are non-abelian dualities mixing everything up in supersymmetric theories, preserving supersymmetry. $\endgroup$ Jul 9 '20 at 16:17

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