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On the possibility of $Z_N$ exotic supersymmetry in two dimensional Conformal Field Theory

F. Ravanini
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Abstract

We investigate the possibility to construct extended parafermionic conformal algebras whose generating current has spin $1+\frac{1}{K}$, generalizing the superconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras. Models invariant under such algebras would possess $Z_K$ exotic supersymmetries satisfying (supercharge)$^K$ = (momentum). However, we show that for $K=4$ this new algebra allows only for models at $c=1$, for $K=5$ it is a trivial rephrasing of the ordinary $Z_5$ parafermionic model, for $K=6,7$ (and, requiring unitarity, for all larger $K$) such algebras do not exist. Implications of this result for existence of exotic supersymmetry in two dimensional field theory are discussed.

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F. Ravanini. 1991-09-30. On the possibility of $Z_N$ exotic supersymmetry in two dimensional Conformal Field Theory. https://doi.org/10.1142/s0217751x92002246

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