Einstein Supergravity and New Twistor String Theories

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N=8 supergravity, another with the spectrum of N=4 supergravity coupled to N=4 super-Yang-Mills, and a family with $N\ge 0$ supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N=0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N=8 and N=4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.