Geometric construction of the r-map: from affine special real to special Kähler manifolds

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2009
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  • Article
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  • We give an intrinsic definition of (affine very) special real manifolds and realise any such manifold M as a domain in affine space equipped with a metric which is the Hessian of a cubic polynomial. We prove that the tangent bundle N = TM carries a canonical structure of (affine) special Kähler manifold. This gives an intrinsic description of the r-map as the map M {mapping} N = TM. On the physics side, this map corresponds to the dimensional reduction of rigid vector multiplets from 5 to 4 space-time dimensions. We generalise this construction to the case when M is any Hessian manifold. © Springer-Verlag 2009.
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  • info:eu-repo/semantics/closedAccess
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oai:www.edit.fis.uni-hamburg.de:publications/5707393c-9f9a-4d04-a569-b85c162b2116