Gravity Amplitudes From Double Bonus Relations

TL;DR

This paper introduces new formulas for tree-level graviton amplitudes in $ =8$ supergravity using advanced recursion relations and bonus relations that leverage amplitude zeroes, revealing potential geometric structures.

Contribution

It presents novel expressions for graviton amplitudes derived from BCFW recursion combined with bonus relations, avoiding cyclic expansions and highlighting permutational symmetry.

Findings

New amplitude formulas using bonus relations and zeroes

Preserves permutational symmetry unlike cyclic approaches

Provides evidence for Grassmannian geometric structures in gravity

Abstract

In this letter we derive new expressions for tree-level graviton amplitudes in $\mathcal{N}=8$ supergravity from BCFW recursion relations combined with new types of bonus relations. These bonus relations go beyond the famous $1/z^2$ behavior under a large BCFW shift, and use knowledge about certain zeroes of graviton amplitudes in collinear kinematics. This extra knowledge can be used in the context of global residue theorems by writing the amplitude in a special form using canonical building blocks. In the NMHV case these building blocks are dressed one-loop leading singularities, the same objects that appear in the expansion of Yang-Mills amplitudes, where each term corresponds to an $R$-invariant. Unlike other approaches, our formula is not an expansion in terms of cyclic objects and does not manifest color-kinematics duality, but rather preserves the permutational symmetry of its building blocks. We also comment on the possible connection to Grassmannian geometry and give some non-trivial evidence of such structure for graviton amplitudes.