Twistor transform inddimensions and a unifying role for twistors

Twistors in four dimensions d=4 have provided a convenient description ofmassless particles with any spin, and this led to remarkable computationaltechniques in Yang-Mills field theory. Recently it was shown that the same d=4twistor provides also a unified description of an assortment of other particledynamical systems, including special examples of massless or massive particles,relativistic or non-relativistic, interacting or non-interacting, in flat spaceor curved spaces. In this paper, using 2T-physics as the primary theory, wederive the general twistor transform in d-dimensions that applies to all cases,and show that these more general twistor transforms provide d dimensionalholographic images of an underlying phase space in flat spacetime in d+2dimensions. Certain parameters, such as mass, parameters of spacetime metric,and some coupling constants appear as moduli in the holographic image whileprojecting from d+2 dimensions to (d-1)+1 dimensions or to twistors. We alsoextend the concept of twistors to include the phase space of D-branes, and givethe corresponding twistor transform. The unifying role for the same twistorthat describes an assortment of dynamical systems persists in general includingD-branes. Except for a few special cases in low dimensions that exist in theliterature, our twistors are new.Comment: LaTeX, 32 pages, v4,v5 minor sign corrections and additional reference