Related papers: Complex Generalized Killing Spinors on Riemannian …
The goal of this paper is to clarify connections between Killing fields of constant length on a Rimannian geodesic orbit manifold $(M,g)$ and the structure of its full isometry group. The Lie algebra of the full isometry group of $(M,g)$ is…
We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of eleven dimensional supergravity. The metric, four form and Killing spinors are determined explicitly, up to an…
Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains…
Let (M^n,g) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T, a 4-form F, a spinorial covariant derivative \nabla depending on \nabla^g, T, F, and a…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
We extend the spinorial geometry techniques developed for the solution of supergravity Killing spinor equations to the kappa symmetry condition for supersymmetric brane probe configurations in any supergravity background. In particular, we…
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…
We have found generic Killing spinor identities which bosonic equations of motion have to satisfy in supersymmetric theories if the solutions admit Killing spinors. Those identities constrain possible quantum corrections to bosonic…
We compute the scalar curvature of 7-dimensional ${G}_2$-manifolds admitting a connection with totally skew-symmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar…
The basic first-order differential operators of spin geometry that are Dirac operator and twistor operator are considered. Special types of spinors defined from these operators such as twistor spinors and Killing spinors are discussed.…
We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the…
The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general…
We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show…
Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere $S^n$. In each of the cases we determine the…
We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are 8-dimensional almost Hermitian spin${}_c$ manifolds. Special cases include…
Let $(M,\omega)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are…
This is a doctoral thesis on the application of techniques originally developed in the programme of characterisation of supersymmetric solutions to Supergravity theories, to finding alternative backgrounds. We start by discussing the…
Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew--symmetric. We show that a compact simply connected symmetric space carries a non--parallel Killing $p$--form ($p\ge2$) if and only if…
We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor…
Suppose $M$ is a closed $n$-dimensional spin$^c$ manifold with spin$^c$ structure $\sigma$ and associated spin$^c$ line bundle $L$. If one fixes a Riemannian metric $g$ on $M$ and a connection $\nabla_L$ on $L$, the generalized scalar…