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Special geometry of Calabi‐Yau compactifications near a rigid limit
Author(s) -
Billó Marco,
Denef Frederik,
Frè Pietro,
Pesando Igor,
Troost Walter,
Van Proeyen Antoine,
Za Daniela
Publication year - 1999
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(199901)47:1/3<133::aid-prop133>3.0.co;2-3
Subject(s) - calabi–yau manifold , riemann surface , limit (mathematics) , physics , string (physics) , decoupling (probability) , string theory , moduli , geometry , mathematical physics , mathematics , mathematical analysis , quantum mechanics , control engineering , engineering
We discuss, in the framework of special Kähler 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 Kähler 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.