Symmetry structure of special geometries

1992/10/13 by B. de Wit, Bernard de Wit, F. Vanderseypen +2 · 10 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/0550-3213(93)90413-j

published as Nucl.Phys. B400 (1993) 463-524 · 48 pp., KUL-TF-92/7 and THU-92/19

arxiv created 1992/10/13 · openalex publication_date 1993/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Broken sigma-model isometries in very special geometry
• The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras

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• The low-energy effective action for perturbative heterotic strings on K3 × T2 and the d = 4 N = 2 vector-tensor multiplet
• R-R scalars, U-duality and solvable Lie algebras
• String loop corrected hypermultiplet moduli spaces
• Charge orbits of extremal black holes in five-dimensional supergravity
• Supergravity black holes and billiards and the Liouville integrable structure associated with Borel algebras