Gravity with a cosmological constant from rational curves

TL;DR

This paper introduces a new, supersymmetric formula for tree-level correlators in gauged N=8 supergravity in AdS_4, expressed via rational maps in twistor space, connecting to flat space amplitudes and recursion relations.

Contribution

It provides a novel, perturbation-theory-independent formula for supergravity correlators in AdS_4 using twistor space and rational maps, applicable to all tree-level cases.

Findings

Formula is polynomial in the cosmological constant.

Equivalent to known perturbative expressions at 3-point and n-point levels.

Respects BCFW recursion and factorization in twistor space.

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.