Gravity with a cosmological constant from rational curves

We give a new formula for all tree-level correlators of boundary field insertions in gauged N=8 supergravity in AdS_4; this is an analog of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann sphere to twistor space, with no reference to bulk perturbation theory. It is polynomial in the cosmological constant, and equal to the classical scattering amplitudes of supergravity in the flat space limit. The formula is manifestly supersymmetric, independent of gauge choices on twistor space, and equivalent to expressions computed via perturbation theory at 3-point MHV-bar and n-point MHV. We also show that the formula factorizes and obeys BCFW recursion in twistor space.