Resultants and Gravity Amplitudes

Understand

Two very different formulations of the tree-level S-matrix of N=8 Einstein supergravity in terms of rational maps are known to exist.

• In both formulations, the computation of a scattering amplitude of n particles in the k R-charge sector involves an integral over the moduli space of certain holomorphic maps of degree d=k-1.
• In this paper we show that both formulations can be simplified when written in a manifestly parity invariant form as integrals over holomorphic maps of bi-degree (d,n-d-2).
• In one formulation the full integrand becomes directly the product of the resultants of each of the two maps defining the one of bi-degree (d,n-d-2).