SUSY Ward identities, Superamplitudes, and Counterterms

Abstract

Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which theseWard identities are solved in N = 4 SYM and N = 8 supergravity. The solution, valid at both tree and loop level, expresses any N[superscript K]MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classi ed 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.