Ward Identities for Superamplitudes

Abstract

We introduce Ward identities for superamplitudes in D-dimensional N-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an $n$-partice superamplitude take a simple universal form for half-BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the $n$ superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by $(D-2) L +2- N$ or $(D-2) L +2- 2 N$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.