One-loop supergravity amplitudes from MHV diagrams

Abstract

We discuss the calculation of one-loop amplitudes in supergravity using MHV diagrams. In this approach, one-loop amplitudes are expressed as sums of MHV diagrams, which incorporate large numbers of Feynman diagrams. In contrast to MHV amplitudes of gluons in Yang–Mills, tree-level MHV amplitudes of gravitons are not holomorphic in the spinor variables. In order to extend these amplitudes off shell, and use them as vertices to build loops, we introduce certain shifts for the spinor variables associated with the loop momenta. Using this off-shell prescription, we rederive in a compact way the four- and five-point MHV amplitudes of gravitons at one loop, in complete agreement with known results. We also discuss the case of one-loop MHV amplitudes with an arbitrary number of gravitons.