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

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

1991-09-30

arxiv.org/abs/hep-th/9109057v1

Int.J.Mod.Phys. A7 (1992) 4949-4964

Physics

High Energy Physics

High Energy Physics - Theory

21pp

Scientific paper

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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