Related papers: Supersymmetric Killing Structures
In physics literature about supersymmetry, many authors refer to "super Minkowski spaces". These spaces are affine supermanifolds with certain distinguished spin structures. In these notes, we make the notion of such spin structures precise…
We study the algebraic structure of the Killing superalgebra of a supersymmetric background of $11$-dimensional supergravity and show that it is isomorphic to a filtered deformation of a $\mathbb Z$-graded subalgebra of the Poincar\'e…
We simplify the classification of supersymmetric solutions with compact holonomy of the Killing spinor equations of heterotic supergravity using the field equations and the additional assumption that the 3-form flux is closed. We determine…
We put into light the Killing vector fields on $\mathbb R^2$ endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lam\'{e} coefficients, we concretely describe the symmetries of the metric.
We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The…
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.…
Geometric Killing spinors which exist on AdS_{p+2} X S^{d-p-2} sometimes may be identified with supersymmetric Killing spinors. This explains the enhancement of unbroken supersymmetry near the p-brane horizon in d dimensions. The…
We employ the language of Cartan's geometry to present a model for studying vector spaces of Killing two-tensors defined in pseudo-Riemannian spaces of constant curvature under the action of the corresponding isometry group. We also discuss…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…
We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local…
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…
We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a…
In this paper nontrivial Killing vector fields of constant length and corresponding flows on smooth complete Riemannian manifolds are investigated. It is proved that such a flow on symmetric space is free or induced by a free isometric…
Admissible curved space backgrounds for four-dimensional supersymmetric field theories are determined by solving Killing spinor equations of four-dimensional off-shell supergravities. These can be obtained by combining ten-dimensional type…
These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half…
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson…
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic…
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations…
We study the near horizon geometry of generic Killing horizons constructing suitable coordinates and taking the appropriate scaling limit. We are able to show that the geometry will always show an enhancement of symmetries, and, in the…