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arXiv · hep-th/9801140

Special geometry of Calabi-Yau compactifications near a rigid limit

Marco Billo·Frederik Denef·Pietro Fre·Igor Pesando·Walter Troost·Antoine Van Proeyen·Daniela Zanon
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Abstract

We discuss, in the framework of special Kahler geometry, some aspects of the "rigid limit" of type IIB string theory compactified on a Calabi-Yau threefold. We outline the general idea and demonstrate by direct analysis of a specific example how this limit is obtained. The decoupling of gravity and the reduction of special Kahler geometry from local to rigid is demonstrated explicitly, without first going to a noncompact approximation of the Calabi-Yau. In doing so, we obtain the Seiberg-Witten Riemann surfaces corresponding to different rigid limits as degenerating branches of a higher genus Riemann surface, defined for all values of the moduli. Apart from giving a nice geometrical picture, this allows one to calculate easily some gravitational corrections to e.g. the Seiberg-Witten central charge formula. We make some connections to the 2/5-brane picture, also away from the rigid limit, though only at the formal level.

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Marco Billo, Frederik Denef, Pietro Fre, Igor Pesando, Walter Troost, Antoine Van Proeyen, Daniela Zanon. 1998-01-20. Special geometry of Calabi-Yau compactifications near a rigid limit. https://doi.org/10.1002/(sici)1521-3978(199901)47%3A1%2F3%3C133%3A%3Aaid-prop133%3E3.0.co%3B2-3

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