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arXiv · hep-th/9210068

Symmetry structure of special geometries

B. de Wit·F. Vanderseypen·A. Van Proeyen
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Abstract

Using techniques from supergravity and dimensional reduction, we study the full isometry algebra of Kähler and quaternionic manifolds with special geometry. These two varieties are related by the so-called c-map, which can be understood from dimensional reduction of supergravity theories or by changing chirality assignments in the underlying superstring theory. An important subclass, studied in detail, consists of the spaces that follow from real special spaces using the so-called r-map. We generally clarify the presence of `extra' symmetries emerging from dimensional reduction and give the conditions for the existence of `hidden' symmetries. These symmetries play a major role in our analysis. We specify the structure of the homogeneous special manifolds as coset spaces $G/H$. These include all homogeneous quaternionic spaces.

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B. de Wit, F. Vanderseypen, A. Van Proeyen. 1992-10-13. Symmetry structure of special geometries. https://doi.org/10.1016/0550-3213(93)90413-j

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