SUSY Ward identities, Superamplitudes, and Counterterms

Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in N = 4 SYM and N = 8 supergravity. The solution, valid at both tree and loop level, expresses any NMHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular N -by-K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in N = 8 supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review. This article is an invited review for a special issue of Journal of Physics A devoted to “Scattering Amplitudes in Gauge Theories”. ar X iv :1 01 2. 34 01 v2 [ he pth ] 6 J ul 2 01 1