Einstein supergravity amplitudes from twistor-string theory

TL;DR

This paper develops a twistor-string formulation for calculating all tree-level amplitudes in Einstein supergravity theories with different supersymmetries and cosmological constants, providing a new geometric approach to these calculations.

Contribution

It introduces a twistor-string framework for Einstein supergravity amplitudes, extending previous conformal gravity results and systematically excluding spurious contributions.

Findings

Formulas for Einstein supergravity amplitudes with N=0 and 4

Extension to N=4 supergravity amplitudes

Comparison with BCFW recursion for N=8 supergravity

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.