Higher Dimensional Classical W-Algebras

Details Higher Dimensional Classical W-Algebras Higher Dimensional Classical W-Algebras

1992-06-09

arxiv.org/abs/hep-th/9206040v1

Commun.Math.Phys. 157 (1993) 573-590

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Plain TeX, KUL-TF-92/19, US-FT/6-92

Scientific paper

10.1007/BF02096883

Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These $W$-algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). The two dimensional case is worked out explicitly and it is shown that the role of Diff$S(1)$ is taken by the algebra of generators of local diffeomorphisms in two dimensions.

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