相关论文: Extended superalgebras from twistor and Killing sp…
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of…
A Killing-Yano tensor is an antisymmetric tensor obeying a first-order differential constraint similar to that obeyed by a Killing vector. In this article we consider generalisations of such objects, focusing on the conformal case. These…
In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit…
We present a result for non-compact manifolds with invertible Dirac operator, where we link the presence of a massless Killing spinor, with a harmonic, closed conformal Killing-Yano tensor, if one exists for the specic manifold. A couple of…
We study the interplay between basic Dirac operator and transverse Killing and twistor spinors. In order to obtain results for general Riemannian foliations with bundle-like metric we consider transverse Killing spinors that appear as…
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the…
Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in…
In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By…
It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY)…
We calculate the Spencer cohomology of the $(1,0)$ Poincar\'e superalgebras in six dimensions: with and without R-symmetry. As the cases of four and eleven dimensions taught us, we may read off from this calculation a Killing spinor…
We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
We show how, for all dimensions and signatures, a symmetry operator for the massless Dirac equation can be constructed from a conformal Killing-Yano tensor of arbitrary degree.
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…
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 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…
We study first BGG operators and their solutions on homogeneous conformal geometries. We focus on conformal Killing tensors, conformal Killing--Yano forms and twistor spinors in particular. We develop an invariant calculus that allows us to…
We derive the most general first order symmetry operator for the Dirac equation coupled to arbitrary fluxes. Such an operator is given in terms of an inhomogenous form omega which is a solution to a coupled system of first order partial…
We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…
We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder…