Ward identities for superamplitudes
Renata Kallosh (Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA, 94305, USA)
We introduce Ward identities for superamplitudes in D-dimensional $$ \mathcal{N} $$ -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 − $$ \mathcal{N} $$ or (D − 2)L + 2 − $$ 2\mathcal{N} $$ , respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.
