Einstein supergravity amplitudes from twistor-string theory

TL;DR

The paper develops a twistor-string framework to produce Einstein gravity tree amplitudes from conformal supergravity data by leveraging Maldacena's argument for nonzero cosmological constant Λ. It introduces infinity twistors to break conformal invariance, establishes a degree–MHV correspondence d=k+1 for Einstein amplitudes, and derives explicit degree-0 and degree-1 results, including a self-dual Einstein action reduction. The authors extend the construction to N=4 and N=8 supergravity, with N=8 amplitudes obtained via BCFW recursion in twistor space, and provide conjectured formulas that reduce correctly to Einstein amplitudes in the Λ→0 limit. They also identify spurious conformal-gravity contributions that must be excluded to isolate Einstein gravity and discuss remaining theoretical challenges, such as worldsheet correlators and a complete N=8 twistor-string description.

Abstract

This paper gives a twistor-string formulation for all tree amplitudes of Einstein (super-)gravities for N=0 and 4. Formulae are given with and without cosmological constant and with various possibilities for the gauging. The formulae are justified by use of Maldacena's observation that conformal gravity tree amplitudes with Einstein wave functions and non-zero cosmological constant will correctly give the Einstein tree amplitudes. This justifies the construction of Einstein gravity amplitudes at N=0 from twistor-string theory and is extended to N=4 by requiring the standard relation between the MHV-degree and the degree of the rational curve for Yang-Mills; this systematically excludes the spurious conformal supergravity gravity contributions. For comparison, BCFW recursion is used to obtain twistor-string-like formulae at degree zero and one (anti-MHV and MHV) for amplitudes with N=8 supersymmetry with and without cosmological constant.