Covariantising the Beltrami equation in W-gravity

Details Covariantising the Beltrami equation in W-gravity Covariantising the Beltrami equation in W-gravity

1995-04-03

arxiv.org/abs/hep-th/9504003v3

Lett.Math.Phys. 37 (1996) 375-383

Physics

High Energy Physics

High Energy Physics - Theory

1+11 pages, LaTeX, version to appear in Lett. Math. Phys

Scientific paper

10.1007/BF00312669

Recently, certain higher dimensional complex manifolds were obtained in [hep-th/9412078] by associating a higher dimensional uniformisation to the generalised Teichm\"uller spaces of Hitchin. The extra dimensions are provided by the ``times'' of the generalised KdV hierarchy. In this paper, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that W-symmetry linearises on these spaces. This is done by explicitly constructing the relationship between the Beltrami differentials which naturally occur in the higher dimensional manifolds and the Beltrami differentials which occur in W-gravity. This also resolves an old puzzle regarding the relationship between KdV flows and W-diffeomorphisms.

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