Related papers: Special geometries, from real to quaternionic
We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole…
Several sets of quaternionic functions are described and studied with respect to hy-perholomorphy, addition and (non commutative) multiplication, on open sets of H, then Hamil-ton 4-manifolds analogous to Riemann surfaces, for H instead of…
A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super…
We review exceptional field theories as the duality-covariant reformulation of maximal supergravity theories in ten and eleven dimensions, that make the underlying exceptional symmetries explicit. Beyond their structural role in unifying…
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\"ahler and quaternionic spaces. This is motivated by the r\^ole these spaces with this symmetry play in $\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to…
A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular…
We construct the most general four-dimensional ${\cal N}=4$ supergravity coupled to an arbitrary number $n$ of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of $\text{SL}(2,\mathbb{R}) \times…
We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies…
A short introduction to N = 1 supergravity in four dimensions in the superspace approach is given emphasising on all steps to obtain the final Lagrangian. In particular starting from geometrical principles and the introduction of…
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…
Half-supersymmetric geometries of N=2 five-dimensional gauged supergravity have recently been fully classified using spinorial geometry techniques. We use this classification to determine all possible regular half-supersymmetric…
We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical…
The half-maximal supergravity theories in three dimensions, which have local $SO(8)\xz SO(n)$ and rigid SO(8,n) symmetries, are discussed in a superspace setting starting from the superconformal theory. The on-shell theory is obtained by…
We construct a topological theory for euclidean gravity in four dimensions, by enforcing self-duality conditions on the spin connection. The corresponding topological symmetry is associated to the SU(2) X diffeomorphism X U(1) invariance.…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic…
Euclidean supersymmetric theories are obtained from Minkowskian theories by performing a reduction in the time direction. This procedure elucidates certain mysterious features of Zumino's N=2 model in four dimensions, provides manifestly…
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…
We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is…