Twistor transform in $d$ dimensions and a unifying role for twistors

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 nonrelativistic, interacting or noninteracting, 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.