Gravity with a cosmological constant from rational curves

TL;DR

The paper tackles the challenge of obtaining a compact, manifestly supersymmetric description of tree-level boundary correlators for gauged $\mathcal{N}=8$ supergravity in $AdS_4$. It introduces a formula based on degree-$d$ rational maps from the Riemann sphere to twistor space, with an infinity twistor encoding the cosmological constant and a twistor-space gauge fixing, yielding an integral kernel that is polynomial in $\Lambda$ and reduces to the flat-space Cachazo-Skinner S-matrix in the $\Lambda\to0$ limit. The construction passes key checks, including gauge invariance, agreement with $\overline{MHV}$ and MHV perturbative results, and twistor-space BCFW recursion, supporting its validity as a compact description of AdS$_4$ gravity correlators. This work suggests deeper twistor-space structures underpin gravity in curved backgrounds and paves the way for connections to twistor-string formulations and generalizations to other AdS backgrounds.

Abstract

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.