2008/05/22 by Massimo Bianchi, Henriette Elvang, Daniel Z. Freedman +1 路 3 citations
Physics and Astronomy 路 #Amplitude #Black Holes and Theoretical Physics #Helicity #Higher-dimensional supergravity #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Spinor #Supergravity #Supersymmetric gauge theory #Supersymmetry #Tree (set theory) #hep-th
paper 路 pdf 路 doi:10.1088/1126-6708/2008/09/063
published as JHEP 0809:063,2008 路 53 pages, 8 figures. v2: Added references, typos corrected
arxiv created 2008/05/22 路 openalex publication_date 2008/09/11 路 arxiv updated 2009/12/01 路 openalex created_date 2016/06/24 路 openalex updated_date 2026/08/05
We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. The recursion relations remain valid for a subset of N=8 supergravity amplitudes which do not vanish asymptotically for all |X]. The MHV-vertex expansion of the n-graviton NMHV amplitude for n=5,6,...,11 is independent of |X] and exhibits the asymptotic behavior zn-12. This presages difficulties for n > 12. Generating functions show how the symmetries of supergravity can be implemented in the quadratic map between supergravity and gauge theory embodied in the KLT and other similar relations between amplitudes in the two theories.