Related papers: Special geometries, from real to quaternionic
We review the construction of higher-form symmetries for supersymmetric theories using a supergeometry framework. This reveals an enlarged set of topological conserved supercurrents, including Chern-Weil symmetries and new geometric…
Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the…
Given a quaternionic manifold $M$ with a certain $\mathrm{U}(1)$-symmetry, we construct a hypercomplex manifold $M'$ of the same dimension. This construction generalizes the quaternionic K\"ahler/hyper-K\"ahler-correspondence. As an example…
I review some ways in which spacetime dimensionality enters explicitly in gravitation. In particular, I recall some unusual geometrical gravity models that are constructible in dimensions different from four, especially in D=3 where even…
Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is…
Relying on the method of spinorial geometry, purely bosonic supersymmetric solutions in N=2, five-dimensional supergravity theories coupled to vector multiplets in all space-time signatures are found. Explicit examples of some new solutions…
This article is based on the author's PhD--thesis. We study geometric transitions on the supergravity level using the basic idea of arXiv:hep-th/0403288, where a pair of non-Kaehler backgrounds was constructed, which are related by a…
We consider rigid supersymmetric theories in four-dimensional Riemannian spin manifolds. We build the Lagrangian directly in Euclidean signature from the outset, keeping track of potential boundary terms. We reformulate the conditions for…
Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
We describe the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental 4-form but are not…
We construct supergravity backgrounds representing non-homogeneous compactifications of d=10,11 supergravities to four dimensions, which cannot be written as a direct product. The geometries are regular and approach $AdS_7\times S^4$ or…
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…
We study the dimensional reduction of the ${\cal N}=1$, ten-dimensional Heterotic Supergravity to four dimensions, at leading order in $\alpha'$, when the internal space is a nearly-K\"{a}hler manifold. Nearly-K\"{a}hler manifolds in six…
The simplest examples of gauged supergravities are N=1 or N=2 theories with Fayet-Iliopoulos (FI) terms. FI terms in supergravity imply that the R-symmetry is gauged. Also the U(1) or SU(2) local symmetries of Kaehler and…
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dimensional standard spheres. The class of such maps also…
Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$…
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…
We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…
Which theories have a higher dimensional origin in String/M-theory is a non trivial question and it is still far from being understood in the constrained scenario of maximal supergravities. After 35 years of progress in this direction we…