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arXiv · hep-th/9209065

Realisations of $W_3$ Symmetry

E. Bergshoeff·H. J. Boonstra·M. de Roo
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Abstract

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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E. Bergshoeff, H. J. Boonstra, M. de Roo. 1992-09-18. Realisations of $W_3$ Symmetry. https://doi.org/10.1016/0370-2693(92)91180-h

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