1205.3500 (Eduardo Conde et al.)

The Anomaly of the Twelve-Graviton Next-to-MHV Risager Amplitude    [PDF]

Eduardo Conde, Sayeh Rajabi

The MHV or CSW expansion of tree-level Yang-Mills amplitudes provides an elegant and simple way of obtaining analytic formulas for S-matrix elements. Inspired by the BCFW technique, a systematic approach to obtain the MHV expansion was introduced by Risager, using a particular complex deformation. Although it works for Yang-Mills amplitudes, Risager's technique fails to provide an MHV expansion already for Next-to-MHV gravity amplitudes with more than eleven particles, as shown by Bianchi, Elvang and Freedman in 2008. This fact implies that in this sector there is a contribution at infinity starting at n = 12, which we call the "Anomaly". In this note we determine the explicit analytic form of the anomaly for n = 12. Together with the terms of the Risager MHV expansion, the anomaly completes the first full CSW-like analytic expression of the twelve-graviton NMHV amplitude. Our technique can also be used to compute the anomaly for higher points.

View original: http://arxiv.org/abs/1205.3500