Gluing Noncommutative Twistor Spaces

Abstract

We describe a general procedure, based on Gerstenhaber-Schack complexes, for extending to quantized twistor spaces the Donaldson-Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on noncommutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.

Twistor sigma models for quaternionic geometry and graviton scattering

“…Clearly, an important challenge is to derive (directly from general relativity) all ingredients of the all MHV-degree generating functional (6.9), and thus give a space-time derivation of the formula (6.15) for the tree-level S-matrix. One could hope that this might correspond to a fully non-linear twistor construction, perhaps following some of the ideas in [69,70], or completing the sigma model to a fully consistent string theory in its own right. It should also be possible to extend the principals underlying this construction to Einstein-Yang-Mills amplitudes, and thereby improve upon the calculations of Yang-Mills amplitudes in strong self-dual background fields in [71].…”

Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

“…It should be recognized here that already did appear several interesting papers dealing with quantum deformations of twistors and their geometries (see e.g. [24]- [30]).…”

“…Such a view, conceptually attractive, however still faces the basic question how looks the appropriate formulation of quantum gravity in space-time picture. On twistorial side some first steps towards the construction of twistorial quantum gravity model was provided in [28] (see also [30]).…”