Twistor Transform in d Dimensions and a Unifying Role for Twistors

TL;DR

This paper generalizes twistor theory to d dimensions using 2T-physics, unifying various particle systems and D-branes within a higher-dimensional holographic framework, revealing new twistor structures.

Contribution

It derives a general d-dimensional twistor transform applicable to diverse systems, extending twistors to D-branes and revealing their holographic images in higher-dimensional space.

Findings

Unified twistor description for various particle systems in d dimensions.

Extension of twistors to include D-brane phase spaces.

Twistor transforms as holographic images in d+2 dimensions.

Abstract

Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same d=4 twistor provides also a unified description of an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. In this paper, using 2T-physics as the primary theory, we derive the general twistor transform in d-dimensions that applies to all cases, and show that these more general twistor transforms provide d dimensional holographic images of an underlying phase space in flat spacetime in d+2 dimensions. Certain parameters, such as mass, parameters of spacetime metric, and some coupling constants appear as moduli in the holographic image while projecting from d+2 dimensions to (d-1)+1 dimensions or to twistors. We also extend the concept of twistors to include the phase space of D-branes, and give the corresponding twistor transform. The unifying role for the same twistor that describes an assortment of dynamical systems persists in general including D-branes. Except for a few special cases in low dimensions that exist in the literature, our twistors are new.