Gravity from Rational Curves in Twistor Space

This Letter presents a new formula which is conjectured to yield all tree amplitudes in $\mathcal{N}=8$ supergravity. The amplitudes are described in terms of higher degree rational maps to twistor space. The resulting expression has manifest $\mathcal{N}=8$ supersymmetry and is manifestly permutation symmetric in all external states. It depends monomially on the infinity twistor that explicitly breaks conformal symmetry to Poincaré symmetry. We have carried out various nontrivial analytic and numerical checks of the formula for up to eight external states with arbitrary helicities.