Beyond Discontinuities: Cosmological WFCs from the Supersymmetric Orthogonal Grassmannian

TL;DR

This paper extends the Grassmannian framework for wave function coefficients in cosmology to include conserved currents by leveraging $ ext{N}=2$ supersymmetry, capturing full coefficients beyond discontinuities.

Contribution

It introduces a supersymmetric Grassmannian formula with a kinematic prefactor that encodes complete wave function coefficients, including conserved currents.

Findings

Supersymmetry relates spinning and non-spinning wave function coefficients.

The formula captures full wave function coefficients, not just discontinuities.

Positive and negative branches correspond to different supersymmetric invariants.

Abstract

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.