Related papers: Superconformal symmetry and hyperKaehler manifolds…

We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local…

Using the harmonic superspace techniques in D=2 N=4, we present an explicit derivation of a new hyper-Kahler metric associated to the Toda like self interaction $H ^{4+}(\omega, u)= (\frac{\xi^{++}}{\lambda})^{2}\exp(2\lambda \omega)$. Some…

An overview of matter-coupled ${\cal N}=2$ supergravity theories with 8 real supercharges, in 4,5 and 6 dimensions is given. The construction of the theories by superconformal methods is explained from basic principles. Special geometry is…

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as…

The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N=2 supergravity in 4 dimensions is denoted as special Kaehler geometry. There are several equivalent definitions, the most elegant ones involve the…

We review non-linear sigma-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2,2) superfields. We provide evidence to support the conjecture that all N=(2,2)…

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The $SU(2)_{local}\times SU(2)_{global}$ N=4 superconformal symmetry of the particle action requires the background to be a…

We present ${\cal N}{=}\,4$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant…

We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler…

We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing…

The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the…

We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the…

We associate to the resolved conifold an affine special K\"{a}hler (ASK) manifold of complex dimension 1, and an instanton corrected hyperk\"{a}hler (HK) manifold of complex dimension 2. We describe these geometries explicitly, and show…

A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-K\"ahler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong…

Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom black holes is shown to admit 4 supersymmetries using an unconventional supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit is found in…

For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of…

In this paper we study the para-hyperK\"ahler geometry of the deformation space of MGHC anti-de Sitter structures on $\Sigma\times\mathbb R$, for $\Sigma$ a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three…

In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization…

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…