Covariantising the Beltrami equation in W-gravity

Govindarajan, Suresh

doi:10.1007/bf00312669

Cited by 2 publications

(18 citation statements)

References 14 publications

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“…It is therefore useful to work out an algorithm to generate this transformation. We hope to address this issue in the future [27].…”

Section: Deformation Of Complex Structurementioning

confidence: 99%

Higher dimensional uniformisation and W-geometry

Govindarajan

1995

Nuclear Physics B

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We formulate the uniformisation problem underlying the geometry of Wn-gravity using the differential equation approach to W -algebras. We construct Wn-space (analogous to superspace in supersymmetry) as an (n − 1) dimensional complex manifold using isomonodromic deformations of linear differential equations. The Wn-manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n, R) which acts properly discontinuously on a simply connected domain in CP n−1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W -diffeomorphisms to (linear) diffeomorphisms on the Wn-manifold. We discuss how the Teichmüller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the Wn-manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all "generic" W-algebras. *

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“…It is therefore useful to work out an algorithm to generate this transformation. We hope to address this issue in the future [27].…”

Section: Deformation Of Complex Structurementioning

confidence: 99%

Higher dimensional uniformisation and W-geometry

Govindarajan

1995

Nuclear Physics B

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“…The general ansatz (6.17) given in [15] and exemplified in (6.22) and (6.33), (6.34) for s = 3, 4 respectively, can be put into relation with some previous pioneer work [6,5,8,10]. Indeed, [10] will be of particular interest.…”

Section: Comparison With Some Previous Workmentioning

confidence: 96%

“…Then, despite the lack of well settled examples in the literature for (even if some examples exist [33,34]) W s (s ≥ 5), remarkable results in [10] will allow to find out a general setting.…”

Section: Jets Versus Tensors or How To Recover W-algebrasmentioning

confidence: 99%

“…Indeed, [10] will be of particular interest. There "Beltrami differentials" emerging from a multi-time approach for KdV flows were related to "Bilal-Fock-Kogan" generalized tensorial Beltrami coefficients [5] appearing in W-gravity along the ideas of [6].…”

Section: Comparison With Some Previous Workmentioning

confidence: 99%

“…We have simply in mind the ideas of, firstly, pursuing further ahead the method given by Forsyth in [14], and secondly, dealing with scalar coordinates considered as solutions of generalized Beltrami equations (see e.g. [8] or [18] appendix C2) just about the approach given in [8,10]. Our motivation for using the inhomogeneous coordinates rests on the fact that they seem to be more natural for constructing projective invariants.…”

Section: Introductionmentioning

confidence: 99%

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Large chiral diffeomorphisms on Riemann surfaces and W-algebras

Bandelloni

Lazzarini

2006

Journal of Mathematical Physics

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The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphims.

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Covariantising the Beltrami equation in W-gravity

Cited by 2 publications

References 14 publications

Higher dimensional uniformisation and W-geometry

Higher dimensional uniformisation and W-geometry

Large chiral diffeomorphisms on Riemann surfaces and W-algebras

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