Integrability vs. Supersymmetry

Details Integrability vs. Supersymmetry Integrability vs. Supersymmetry

1996-08-29

arxiv.org/abs/hep-th/9608190v2

Phys.Lett. B389 (1996) 665-672

Physics

High Energy Physics

High Energy Physics - Theory

plain TeX file, 11 pages output, macros included; minor errors corrected, extra references added

Scientific paper

10.1016/S0370-2693(96)01503-1

We investigate (1,0)-superconformal Toda theories based on simple Lie algebras and find that the classical integrability properties of the underlying bosonic theories do not survive. For several models based on algebras of low rank, we show explicitly that none of the conserved W-algebra generators can be generalized to the supersymmetric case. Using these results we deduce that at least one W-algebra generator fails to generalize in any model based on a classical Lie algebra. This argument involves a method for relating the bosonic Toda theories and their conserved currents within each classical series. We also scrutinize claims that the (1,0)-superconformal models actually admit (1,1) supersymmetry and find that they do not. Our results are consistent with the belief that all integrable Toda models with fermions arise from Lie superalgebras.

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