Related papers: Spinor equations in Weyl geometry

In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $ SL(n, R) $ -structure and discuss possible applications of…

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows $M$ carrying non-trivial solutions to that equation in case $M$ is a local Riemannian product,…

We consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed two-form that is invariant under the Lie algebra of conformal Killing vectors.…

We consider the wave equation for spinors in ${\cal D}$-dimensional Weyl geometry. By appropriately coupling the Weyl vector $\phi _{\mu}$ as well as the spin connection $\omega _{\mu a b } $ to the spinor field, conformal invariance can be…

The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…

We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional $\mathcal{N}=1$ supergravity coupled to a chiral non-linear sigma model and a Spin$^{c}_0$ structure. The model involves a…

This paper is the second one of a series of three and it is the continuation of math-ph/0412074. We review some properties of the algebraic spinors in Cl(3,0) and Cl(0,3) and how Weyl, Pauli and Dirac spinors are constructed in Cl(3,0) (and…

We show that solutions of the Seiberg-Witten equations lead to non-trivial lower bounds for the L2-norm of the Weyl curvature of a compact Riemannian 4-manifold. These estimates are then used to derive new obstructions to the existence of…

Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless,…

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of…

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 spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the…

We show that $3$-$(\alpha,\delta)$-Sasaki manifolds admit solutions of a certain new spinorial field equation (the $\mathcal{H}$-Killing equation) generalizing the well-known Killing spinors on $3$-Sasakian manifolds. These…

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In…

For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*} \left\{ \begin{array}{ll} D\varphi = \lambda f\varphi & \text{in } M, \\ \mathbf{B}\varphi = 0 & \text{on } \partial M,…

We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian of the Weyl tensor. On oriented manifolds, we also construct natural…

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…

We derive the necessary and sufficient conditions under which the general Plebanski-Demianski (PD) solution of Einstein-Maxwell theory with a negative cosmological constant admits Killing spinors. We consider in detail two different scaling…

We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones…

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and…