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Are there no-go theorems and the like proving that there is no generalization of supersymmetry to fractional spins either in general or for superstrings in four dimensions? If so, are there limitations on what kind of fractional statistics superstrings can acquire if they are confined to 3+1D (like in the fractional quantum Hall effect)? Also, can anyons be defined on open strings? And finally, do string anyons come in both Abelian and non-Abelian varieties?

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    $\begingroup$ Generalization of spin to fractional spin is possible in two or fewer spacetime dimensions. Do you mean fractional supersymmetry on worldsheet? $\endgroup$
    – Nikita
    Dec 27, 2019 at 15:35

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