Einstein supergravity amplitudes from twistor-string theory

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 wavefunctions 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 0 and 1 (anti-MHV and MHV) for amplitudes with {N}=8 supersymmetry with and without cosmological constant.