Covariantising the Beltrami equation in W-gravity
نویسندگان
چکیده
Recently, certain higher dimensional complex manifolds were obtained in [1] by associating a higher dimensional uniformisation to the generalised Teichmüller 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 Wsymmetry 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. Dedicated to the memory of Claude Itzykson E-mail: [email protected]
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Characteristic Equations & Applications
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