Realisations of $W_3$ Symmetry

Details Realisations of $W_3$ Symmetry Realisations of $W_3$ Symmetry

1992-09-18

arxiv.org/abs/hep-th/9209065v1

Phys.Lett. B292 (1992) 307-314

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LATEX, UG-6/92

Scientific paper

10.1016/0370-2693(92)91180-H

We perform a systematic investigation of free-scalar realisations of the Za\-mo\-lod\-chi\-kov $W_3$ algebra in which the operator product of two spin-three generators contains a non-zero operator of spin four which has vanishing norm. This generalises earlier work where such an operator was required to be absent. By allowing this spin-four null operator we obtain several realisations of the $W_3$ algebra both in terms of two scalars as well as in terms of an arbitrary number $n$ of free scalars. Our analysis is complete for the case of two-scalar realisations.

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