Gravity in Twistor Space and its Grassmannian Formulation

Abstract

We prove the formula for the complete tree-level $S$-matrix of $\mathcal{N}=8$ supergravity recently conjectured by two of the authors. The proof proceeds by showing that the new formula satisfies the same BCFW recursion relations that physical amplitudes are known to satisfy, with the same initial conditions. As part of the proof, the behavior of the new formula under large BCFW deformations is studied. An unexpected bonus of the analysis is a very straightforward proof of the enigmatic $1/z^2$ behavior of gravity. In addition, we provide a description of gravity amplitudes as a multidimensional contour integral over a Grassmannian. The Grassmannian formulation has a very simple structure; in the N${}^{k-2}$MHV sector the integrand is essentially the product of that of an MHV and an $\overline{\mathrm{MHV}}$ amplitude, with $k+1$ and $n-k-1$ particles respectively.

References in corpus (13)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Taming Tree Amplitudes In General Relativity
• Gravity from Rational Curves
• Tree Level Recursion Relations In General Relativity
• Twistor Actions for Self-Dual Supergravities
• A simple formula for gravitational MHV amplitudes
• From Twistor String Theory To Recursion Relations
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Three Applications of a Bonus Relation for Gravity Amplitudes
• A Direct Proof of BCFW Recursion for Twistor-Strings
• On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
• A Link Representation for Gravity Amplitudes
• New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits

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