New expressions for gravitational scattering amplitudes
Andrew Hodges
TL;DR
The paper tackles the challenge of expressing and computing tree-level gravitational amplitudes in a way that preserves symmetries and is computationally tractable. It develops a novel $N=7$ supersymmetric BCFW recursion grounded in twistor geometry, eliminating spurious double poles and yielding streamlined MHV and NMHV expressions, with a momentum-twistor formulation that reveals a compact numerator structure. It connects these results to BGK and KLT relations, demonstrates emergent geometric and symmetry features (notably $S_{n-2}$ in certain cases), and proposes a general, order-independent twistor-numerator framework for gravity amplitudes. Together, these advances offer new computational tools and a deeper geometric perspective on gravitational scattering that may guide future higher-point and loop analyses.
Abstract
New methods are introduced for the description and evaluation of tree-level gravitational scattering amplitudes. An N=7 super-symmetric recursion, free from spurious double poles, gives a more efficient method for evaluating MHV amplitudes. The recursion is naturally associated with twistor geometry, and thereby gives a new interpretation for the amplitudes. The recursion leads to new expressions for the MHV amplitudes for six and seven gravitons, simplifying their symmetry properties, and suggesting further generalization. The N=7 recursion is valid for all tree amplitudes, and we illustrate it with a simplified expression for the six-graviton NMHV amplitude. Further new structure emerges when MHV amplitudes are expressed in terms of momentum twistors.