Beyond Discontinuities: Cosmological WFCs from the Supersymmetric Orthogonal Grassmannian
Yu-tin Huang, Chia-Kai Kuo, Yohan Liu, Jiajie Mei
TLDR
This paper uses N=2 supersymmetry to extend the Grassmannian description of cosmological wave function coefficients, capturing full WFCs beyond just discontinuities.
Key contributions
- Relates spinning and non-spinning cosmological WFCs using $\mathcal{N}=2$ supersymmetry.
- Augments the Grassmannian formula with a kinematic prefactor to capture full WFCs, solving inhomogeneous Ward identities.
- Interprets positive and negative branches of the formula as distinct supersymmetric invariants.
- Shows these branches lead to distinct helicity amplitudes in the flat-space limit.
Why it matters
Previous Grassmannian models for cosmological WFCs only captured discontinuities of conserved currents. This paper uses $\mathcal{N}=2$ supersymmetry to provide a complete Grassmannian formula, capturing full WFCs and advancing cosmology.
Original 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.
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