Gravity in Twistor Space and its Grassmannian Formulation

TL;DR

This paper proves a new formula for tree-level supergravity scattering amplitudes, demonstrating its consistency with known recursion relations and providing a Grassmannian integral representation that simplifies the structure of gravity amplitudes.

Contribution

It introduces a novel formula for supergravity amplitudes that satisfies BCFW recursion and offers a simple Grassmannian integral formulation, advancing understanding of gravity scattering.

Findings

The new formula satisfies BCFW recursion relations.

The behavior under large BCFW deformations is clarified.

Gravity amplitudes can be expressed as a Grassmannian contour integral.

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 $\overline{{\rm MHV}}$ amplitude, with $k+1$ and $n-k-1$ particles respectively.