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What is Special K\"ahler Geometry ?

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arxiv hep-th/9703082 v2 pith:2HW7375V submitted 1997-03-11 hep-th

B. Craps , F. Roose , W. Troost , A. Van Proeyen This is my paper · ORCID
classification hep-th
keywords geometryspecialdefinitionskaehlersomesupersymmetryahlerbasis
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The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.

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Cited by 3 Pith papers

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