Special geometry and symplectic transformations

Abstract

Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.

11 pages, latex using espcrc2, no figures. Some factors and minor corrections. Version to be published in the proceedings of the Spring workshop on String theory, Trieste, April 1995

References in corpus (6)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• Perturbative Couplings of Vector Multiplets in $N=2$ Heterotic String Vacua
• On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory
• Pseudo-Duality

Cited by in corpus (15)

• On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes
• Classical and quantum N=2 supersymmetric black holes
• Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points
• N=8 supersymmetric mechanics on special Kähler manifolds
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• Hypermultiplet metric and D-instantons
• Introduction to supergravity
• Vector multiplets in N=2 supersymmetry and its associated moduli spaces
• Zero-branes and the symplectic hypermultiplets
• Half-BPS cosmic string in N=2 supergravity in the presence of a dilaton
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity
• BPS one-branes in five dimensions
• Calabi-Yau compactification of type II string theories
• The geodesic structure of BPS one-branes in five dimensions