Scattering amplitudes and BCFW recursion in twistor space
Abstract
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the threepoint seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for nparticle MHV and NMHV superamplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N^{2}MHV superamplitude. We also give simple closed form formulae for the mathcal{N} = 8 supergravity recursion and the MHV and overline {text{MHV}} amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N^{ k }MHV, the amplitudes are given by 2 n  4 integrals in the form of Hilbert transforms of a product of n  k  2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for treelevel amplitudes in mathcal{N} = 4 super YangMills, and we trace their origin to a topological property of split signature spacetime. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of ArkaniHamed, Cachazo, Cheung and Kaplan.
 Publication:

Journal of High Energy Physics
 Pub Date:
 January 2010
 DOI:
 10.1007/JHEP01(2010)064
 arXiv:
 arXiv:0903.2083
 Bibcode:
 2010JHEP...01..064M
 Keywords:

 Supersymmetric gauge theory;
 Duality in Gauge Field Theories;
 High Energy Physics  Theory
 EPrint:
 v2: minor corrections + extra refs. v3: further minor corrections, extra discussion of signature issues + more refs