ASK/PSK-correspondence and the r-map
We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative \(\alpha '\)-corrections in heterotic and type II string compactifications with \(N=2\) supersymmetry. Also affine special Kähler manifolds with quadratic prepotential are mapped to one-parameter families of projective special Kähler manifolds with quadratic prepotential. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.
KeywordsSpecial real manifolds Special Kähler manifolds r-map
Mathematics Subject Classification53C26 (primary)
This work was partly supported by the German Science Foundation (DFG) under the Research Training Group 1670 and the Collaborative Research Center (SFB) 676. The work of T.M. was partly supported by the STFC consolidated grant ST/G00062X/1. He thanks the Department of Mathematics and the Centre for Mathematical Physics of the University of Hamburg for support and hospitality during various stages of this work.
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