1207.3602 (Tim Adamo et al.)

Twistor-strings and gravity tree amplitudes    [PDF]

Tim Adamo, Lionel Mason

Recently we proposed that the original Berkovits-Witten twistor-string theory could be used to compute Einstein supergravity tree amplitudes. Subsequently remarkable formulae for the MHV amplitudes were found by Hodges and generalized to N^{k}MHV by Cachazo and Skinner. Here we show how the Hodges matrix and its higher MHV degree generalization can be understood as arising from the twistor-string formula. In particular we see that if loops are allowed in the worldsheet correlators, the wrong answers are obtained. On the other hand the Hodges matrix and its generalizations arise when only connected trees are allowed by using the Matrix-Tree theorem to sum up the Feynman diagrams for the worldsheet correlators in the twistor-string theory. Other ingredients in these formulae remain to be properly understood within the twistor-string theory approach.

View original: http://arxiv.org/abs/1207.3602