Related papers: The Definitions of Special Geometry
We show that for all very special quaternionic manifolds a different N=1 reduction exists, defining a Kaehler Geometry which is ``dual'' to the original very special Kaehler geometry with metric G_{a\bar{b}}= - \partial_a \partial_b \ln V…
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2…
We construct non-Abelian N=2 on-shell vector multiplets in five and in four dimensions. Closing of the supersymmetry algebra imposes dynamical constraints on the fields, and these constraints should be interpreted as equations of motion. If…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
We describe special Ka\"hler geometry, special quaternionic manifolds, and very special real manifolds and analyze the structure of their isometries. The classification of the homogeneous manifolds of these types is presented.
We apply the techniques of special Kaehler geometry to investigate AdS_4 vacua of general N=2 gauged supergravities underlying flux compactifications of type II theories. We formulate the scalar potential and its extremization conditions in…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain $N=2$ supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler…
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…
We study two-dimensional N=2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity.
Using superspace techniques we construct the general theory describing D=4, N=2 supergravity coupled to an arbitrary number of vector and scalar--tensor multiplets. The scalar manifold of the theory is the direct product of a special…
A symplectically invariant definition of special K\"ahler geometry is discussed. Certain aspects hereof are illustrated by means of Calabi-Yau moduli spaces.
An $N=2$ supersymmetric model using K\"{a}hler fields is proposed. It is a modified version of two-dimensional Benn-Tucker model. It indicates a geometrical origin of $N=2$ supersymmetry.
We show that the isometries of the manifold of scalars in $N=2$ supergravity in $d=5$ space-time dimensions can be broken by the supergravity interactions. The opposite conclusion holds for the dimensionally reduced $d=4$ theories, where…
In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective…
Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…
We discuss the deformed sigma-model that arises when considering four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry…
We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be…
We construct N=2 four and five-dimensional supergravity theories coupled to vector multiplets in various space-time signatures (t,s), where t and s refer, respectively, to the number of time and spatial dimensions. The five-dimensional…
In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in…