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Showing 1 to 16 of 16 for “"Twistor"”.
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Newtonian Twistor Theory
In twistor theory the nonlinear graviton construction realises four-dimensional antiself- dual Einstein manifolds as Kodaira moduli spaces of rational curves in threedimensional complex manifolds. We establish a Newtonian analogue of this procedure, in which four-dimensional Newton-Cartan manifolds …
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Twistor Space and Celestial Holography
… more depth. The second part is a discussion of twistor methods for H$^3_\mathbb{C}$ and H$^5_\mathbb{C}$, the complexification of 3 and 5 dimensional hyperbolic space. We discuss the minitwistor space of the bulk and its relation to the ambitwistor space of the boundary. The third part of my …
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SPECIAL RIEMANNIAN STRUCTURES ON FOUR-MANIFOLDS: FROM TWISTOR SPACES TO UNOBSTRUCTED CONDITIONS
… first part of the work, we introduce Riemannian twistor spaces, which are 6-dimensional manifolds which can be associated to any Riemannian four-manifold: these spaces can be endowed with two natural almost Hermitian structures, which are strictly linked to the geometry of the underlying …
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Celestial Chiral Algebras and Self-Dual Gravity
… these celestial chiral algebras in the light of twistor theory and derives tree-level deformations thereof induced by non-trivial background geometries that solve some form of the self-dual Einstein equations. After an elaborate introduction, we begin by reviewing how holomorphic collinear …
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Integrability from Chern-Simons theories
… between holomorphic Chern-Simons theory on twistor space, 4d Chern-Simons theory and the anti-self-dual Yang-Mills equations. Part one opens with a review of 4d Chern-Simons theory, including a discussion of its connections to both quantum and classical integrable systems. It then turns to …
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Aspects of twistors and tractors in field theory
… The second concerns the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS_5 is the same as the ambitwistor space of the four-dimensional conformal boundary; the geometry of this correspondence is reviewed for both the bulk and boundary. A …
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Geometry of SU(3) Manifolds
… or compact admissible examples, I study the twistor spaces of Riemannian 4-manifolds. It turns out that twistor spaces over self-dual Einstein 4-manifolds provide admissible and nearly Calabi-Yau manifolds. I also construct some explicit special Lagrangian examples in nearly K\"ahler …
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The projective to Einstein correspondence and a kink on a wormhole
… curvature, and are thus associated with a twistor space. In the presence of a symmetry, they can be reduced to Einstein-Weyl structures in dimension three via the Jones–Tod correspondence. Because $M$ is also Einstein with non–zero scalar curvature, these Einstein–Weyl structures are …
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2D Chiral Algebras from Koszul Duality & Associativity
… must admit a local gauge-anomaly-free lift to twistor space. We will also use Koszul duality in a different context, the AdS/CFT correspondence, to determine the planar chiral algebra for a certain supersymmetric CFT. This provides a new and analytic method to completely determine the 2 and …
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Études in Ambitwistor Strings - Exploring new models, higher loops and curved backgrounds
… scattering equations, CHY formalism and the ambitwistor string. We discuss one of the striking simplifications that occur upon restricting to four spacetime dimensions, namely that the scattering equations with $n$ particles decompose into sectors, graded by an integer $1 \leq d \leq n-3$. It is …
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Anti-self-dual fields and manifolds
… function subject to Przanowski’s equation. Using twistorial methods we construct a Lax Pair for Przanowski’s equation, confirming its integrability. The Lee form of a compatible local complex structure gives rise to a conformally invariant differential operator, special cases of the associated …
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Vortices, Painlevé integrability and projective geometry
… in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the …
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Stability, Range and Statistical Aspects of non-Abelian X-ray tomography
… normal operators. Finally, we introduce a novel twistor correspondence in dim M = 2, under which (M,g) corresponds to a complex surface Z and attenuations A correspond to holomorphic vector bundles over Z. We show that the twistor space Z of a simple surface behaves in many ways like a …
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AdS3 Holography from the Worldsheet
… naturally understood as a sigma model on the minitwistor space of $AdS_3$. The incidence relations are studied, showing how they encode both bulk and boundary physics simultaneously. The sigma model we present has several important differences with conventional twistor string constructions, most …
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Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity.
… years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology …
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Worldsheet methods for perturbative quantum field theory
… The first part concerns the study of the ambitwistor string and the scattering equations, while the second concerns the interplay of the symmetries of the asymptotic null boundary of Minkowski space, called $\scri$, and scattering amplitudes. The first part begins with a review of the CHY …