Twistor transform of all tree amplitudes in N=4 SYM theory

Details Twistor transform of all tree amplitudes in N=4 SYM theory Twistor transform of all tree amplitudes in N=4 SYM theory

2009-07-23

arxiv.org/abs/0907.4107v1

Nucl.Phys.B829:478-522,2010

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, 17 figures

Scientific paper

10.1016/j.nuclphysb.2009.11.017

We perform the twistor (half-Fourier) transform of all tree n-particle superamplitudes in N=4 SYM and show that it has a transparent geometric interpretation. We find that the N^kMHV amplitude is supported on a set of (2k+1) intersecting lines in twistor space and demonstrate that the corresponding line moduli form a lightlike (2k+1)-gon in moduli space. This polygon is triangulated into two kinds of lightlike triangles lying in different planes. We formulate simple graphical rules for constructing the triangulated polygons, from which the analytic expressions of the N^kMHV amplitudes follow directly, both in twistor and in momentum space. We also discuss the ordinary and dual conformal properties and the cancellation of spurious singularities in twistor space.

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