Beyond Discontinuities: Cosmological WFCs from the Supersymmetric Orthogonal Grassmannian

Recently, it has been shown that wave function coefficients (WFCs) admit a natural description in terms of the orthogonal Grassmannian, furnishing homogeneous solutions to the three-dimensional conformal Ward identities in spinor-helicity variables. This, however, presents a challenge for WFCs of conserved currents, which satisfy inhomogeneous Ward identities; correspondingly, the Grassmannian construction reproduces only their \textit{discontinuities}. In this paper, we show that $\mathcal{N}=2$ supersymmetry, by relating spinning and non-spinning WFCs, leads to a Grassmannian formula augmented by a kinematic prefactor that captures the full WFC. Moreover, we show that the positive and negative branches of the Grassmannian formula admit a natural interpretation in terms of supersymmetric invariants, and give rise to distinct helicity amplitudes in the flat-space limit.