Related papers: Twistor theory and the harmonic hull
This is the first part in a series of three articles in which are studied the domains of monogenicity for the $n$-Cauchy-Fueter operator. Using the twistor theory, we will in this article show that for a given open subset $U$ of…
Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic $SL(2, \C)$…
It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.
The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.
This is a review of recent developments in the study of perturbative gauge theory and gravity using action functionals on twistor space. It is intended to provide a user-friendly introduction to twistor actions, geared towards researchers…
A generalized twistor transform for spinning particles in 3+1 dimensions is constructed that beautifully unifies many types of spinning systems by mapping them to the same twistor, thus predicting an infinite set of duality relations among…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains \Omega\ of R^4. When \Omega\ is a symmetric slice domain, the twistor transform of such a function is a…
We consider superstring sigma models that are based on coset superspaces G/H in which H arises as the fixed point set of an order-4 automorphism of G. We show by means of twistor theory that the corresponding first-order system, consisting…
The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory of weights for various things surrounding…
Four-dimensional conformal fishnet theory is an integrable scalar theory which arises as a double scaling limit of $\gamma$-deformed maximally supersymmetric Yang-Mills. We give a perturbative reformulation of $\gamma$-deformed…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
We introduce the notion of Riemannian twistorial structure and we show that it provides new natural constructions of harmonic maps.
I review recent progress in using twistor-inspired methods to compute perturbative scattering amplitudes in gauge theory, for application to collider physics.
By utilizing the gauge symmetries of Two-Time Physics (2T-physics), a superstring with linearly realized global SU(2,2|4) supersymmetry in 4+2 dimensions (plus internal degrees of freedom) is constructed. It is shown that the dynamics of…
We analyze the twistor space structure of certain one-loop amplitudes in gauge theory. For some amplitudes, we find decompositions that make the twistor structure manifest; for others, we explore the twistor space structure by finding…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…
Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…