Related papers: Harmonic spinors from twistors and potential forms
We study in a general way the construction of string bit Hamiltonians which are supersymmetric, We construct several quadratic and quartic polynomials in string bit creation and annihilation operators ${\bar\phi}^A_{a_1\cdots a_n}$,…
We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature $(1,1)$. We will investigate the properties of the solutions of these equations and try to…
We study the Dirac-Yang-Mills equations on closed spin manifolds with a focus on uncoupled solutions, i.e. solutions for which the connection form satisfies the Yang-Mills equation. Such solutions require the Dirac current, a quadratic form…
We study Kohn-Dirac operators $D_\theta$ on strictly pseudoconvex CR manifolds with ${\rm spin}^{\mathbb C}$ structure of weight $\ell\in{\mathbb Z}$. Certain components of $D_\theta$ are CR invariants. We also derive CR invariant twistor…
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory…
We find exact solutions for N=2 supersymmetric SO(N), N=7,9,10,11,12 gauge theories with matter in the fundamental and spinor representation. These theories, with specific numbers of vectors and spinors, arise naturally in the…
We construct the twisted covariant form hierarchies (TCFH) of (massive) type IIA supergravity for common sector, D-brane and warped product AdS supersymmetric backgrounds and show that the Killing spinor bilinears satisfy a generalisation…
We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many…
The continuous and discrete symmetries of the Dirac-type operators produced by particular Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The Killing-Yano tensors considered are covariantly constant and realize…
We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used…
We show that harmonic spinors obey a strengthened version of the well-known pointwise Kato inequality for sections of a vector bundle with a connection. We then prove a decay estimate for eigenspinors using this Kato-Yau estimate and…
Conformal Killing-Yano tensors are introduced as a generalization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of…
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 introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
I review a recently proposed method for determining the symmetry superalgebra of a supergravity configuration from its Killing spinors, and its application to the `near-horizon' limits of various rotating and intersecting branes.
We consider conformal Killing-Yano forms corresponding to the antisymmetric generalizations of conformal Killing vectors to higher degree forms in the presence of skew-symmetric torsion. Integrability conditions for torsionful conformal…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…