Related papers: Harmonic spinors from twistors and potential forms
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal…
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting…
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.…
Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found.…
In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential…
Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified…
Generalization of twistor spinors to K\"ahler manifolds which are called K\"ahlerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of K\"ahlerian twistor spinors. We show that the bilinear…
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…
Hodge theorem and harmonic spinors are studied in a physics-oriented approach in the present paper. New mathematical results on the harmonic spinors are as follows. Harmonic spinors defined by partial differential operators could be of two…
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.
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…
Modifications of Dirac operators in supergravity flux backgrounds are considered. Modified spin curvature operators and squares of modified Dirac operators corresponding to Schr\"odinger-Lichnerowicz-like formulas are obtained for different…
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability…
We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric…
This paper is a mixture of expository material and current research material. Among new results are examples of generalised harmonic spinors and their gauged version, the generalised Seiberg-Witten equations.
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…
By lifting full Yang-Mills theory to $R_4 \times S_2$, Mason et al. obtained MHV vertices by gauge transformation. Their Lagrangian depended on long intricate twistor manipulations. Spinor $S_2$ harmonics give a one page proof, eliminating…
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…
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many…
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…