Covariantising the Beltrami equation in W-gravity |
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Authors: | Suresh Govindarajan |
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Affiliation: | (1) Theoretical Physics Group, Tata Institute of Fundamental Research, 400 005 Bombay, India;(2) Present address: Department of Physics, Indian Institute of Technology, 600036 Madras, India |
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Abstract: | Recently, certain higher-dimensional complex manifolds were obtained by S. Govindarajan [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 Letter, 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 flow. and W-diffeomorphisms.Dedicated to the memory of Claude Itzykson. |
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Keywords: | Primary: 81T40 secondary: 35Q53 32G05 |
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