arxiv: 2604.08512 · v1 · submitted 2026-04-09 · ✦ hep-th

Recognition: unknown

Beyond Discontinuities: Cosmological WFCs from the Supersymmetric Orthogonal Grassmannian

Yu-tin Huang , Chia-Kai Kuo , Yohan Liu , Jiajie Mei

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:14 UTC · model grok-4.3

classification ✦ hep-th

keywords wave function coefficientsorthogonal GrassmannianN=2 supersymmetrycosmological correlatorsconformal Ward identitiesdiscontinuitieshelicity amplitudes

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The pith

N=2 supersymmetry augments the orthogonal Grassmannian formula with a kinematic prefactor to obtain full cosmological wave function coefficients.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that wave function coefficients in cosmology, previously limited to their discontinuities in the orthogonal Grassmannian approach for conserved currents due to inhomogeneous conformal Ward identities, can be fully captured by incorporating N=2 supersymmetry. This supersymmetry relates spinning and non-spinning versions of these coefficients, allowing the addition of a simple kinematic prefactor to the existing Grassmannian expression. A sympathetic reader would care because this provides a more complete, symmetry-based way to compute or understand these quantities that appear in the early universe's quantum fluctuations. It bridges the gap between the homogeneous solutions from Grassmannians and the full inhomogeneous cases required for physical currents.

Core claim

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, 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.

What carries the argument

The augmented orthogonal Grassmannian formula with a kinematic prefactor derived from N=2 supersymmetric relations between spinning and non-spinning wave function coefficients.

If this is right

The full wave function coefficients for conserved currents, including the inhomogeneous parts, are now obtainable from the Grassmannian construction.
The positive and negative branches correspond to distinct supersymmetric invariants.
These lead to different helicity amplitudes when taking the flat-space limit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This construction could simplify calculations of higher-point correlation functions in de Sitter space by providing closed-form expressions.
Testing the flat-space limits against known scattering amplitudes would provide further validation.

Load-bearing premise

The supersymmetric relations between spinning and non-spinning WFCs hold without additional corrections when applied to the cosmological setting, allowing the Grassmannian formula to extend directly via the prefactor.

What would settle it

An independent computation of a specific three-point or four-point WFC for a conserved current using conformal Ward identities or other techniques, then checking whether the Grassmannian expression plus the proposed kinematic prefactor reproduces the exact full coefficient including the non-discontinuity part.

read the 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

N=2 supersymmetry lets them augment the orthogonal Grassmannian with a kinematic prefactor to get the full wave-function coefficients for conserved currents instead of just discontinuities.

read the letter

The main thing to know is that N=2 supersymmetry relates spinning and non-spinning wave-function coefficients, allowing an augmentation of the orthogonal Grassmannian formula with a kinematic prefactor that captures the full inhomogeneous solutions for conserved currents. This is new compared to the prior Grassmannian work, which only got the discontinuities. The paper does a good job interpreting the positive and negative branches as supersymmetric invariants and confirming that their flat-space limits give distinct helicity amplitudes. Those limits provide a useful cross-check against known results. The derivation stays consistent internally by using the supersymmetric relations to bring in the homogeneous solutions without extra counterterms. No obvious circularity or invented entities here. A minor soft spot is the assumption that the SUSY relations hold in the cosmological background without further corrections. The prefactor is meant to handle the main effects, but it would help to see how robust this is under small perturbations or in explicit examples. This is for specialists in cosmological correlators and Grassmannian techniques within hep-th. Readers working on inflationary model building or higher-point functions with conserved currents will find it directly relevant. I would recommend putting it through peer review. The core argument is clear, the checks are there, and it builds productively on existing literature.

Referee Report

0 major / 2 minor

Summary. The paper claims that N=2 supersymmetry relates spinning and non-spinning wave-function coefficients (WFCs), allowing the orthogonal Grassmannian formula (previously limited to discontinuities) to be augmented by a kinematic prefactor that solves the full inhomogeneous three-dimensional conformal Ward identities for conserved currents. The positive and negative branches of the Grassmannian are interpreted as supersymmetric invariants, and both are shown to reproduce distinct helicity amplitudes in the flat-space limit.

Significance. If the central derivation holds, the result is significant: it furnishes a systematic, supersymmetry-based route to complete cosmological WFCs for spinning fields, extending recent Grassmannian constructions beyond the homogeneous sector and providing explicit control over the inhomogeneous contributions without additional counterterms. This could streamline bootstrap computations in de Sitter space and clarify the structure of correlation functions involving conserved currents.

minor comments (2)

The explicit form of the kinematic prefactor and the precise supersymmetric map between spinning and non-spinning WFCs should be stated in a dedicated equation early in the derivation section to make the augmentation step self-contained.
The flat-space limit discussion would benefit from a short table or explicit helicity-amplitude expressions for both branches to allow immediate comparison with known results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive summary of our work and for recommending minor revision. We are pleased that the potential significance of the result for systematic constructions of cosmological wave-function coefficients is recognized.

read point-by-point responses

Referee: The paper claims that N=2 supersymmetry relates spinning and non-spinning wave-function coefficients (WFCs), allowing the orthogonal Grassmannian formula (previously limited to discontinuities) to be augmented by a kinematic prefactor that solves the full inhomogeneous three-dimensional conformal Ward identities for conserved currents. The positive and negative branches of the Grassmannian are interpreted as supersymmetric invariants, and both are shown to reproduce distinct helicity amplitudes in the flat-space limit.

Authors: We thank the referee for this accurate encapsulation of the manuscript's central claims. The summary correctly identifies how N=2 supersymmetry is used to relate the spinning and non-spinning sectors, thereby supplying the kinematic prefactor needed to satisfy the inhomogeneous Ward identities, and how the two branches of the Grassmannian are interpreted as supersymmetric invariants with distinct flat-space limits. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central step uses N=2 supersymmetry to relate spinning and non-spinning WFCs, thereby augmenting an existing orthogonal Grassmannian formula (which solves homogeneous Ward identities) with a kinematic prefactor that captures the full inhomogeneous solution. This relation is presented as an independent input from supersymmetry, verified by matching flat-space helicity amplitudes and interpreting positive/negative branches as supersymmetric invariants. No equation reduces by construction to a fitted parameter, renamed input, or self-citation chain; the prefactor is derived from the SUSY mapping rather than assumed to match the target WFC. The derivation remains self-contained and introduces new content beyond the prior Grassmannian discontinuities.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on prior Grassmannian constructions for WFCs and standard properties of N=2 supersymmetry; no free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption Orthogonal Grassmannian furnishes homogeneous solutions to three-dimensional conformal Ward identities in spinor-helicity variables
Invoked as the starting point from recent results mentioned in the abstract.
domain assumption N=2 supersymmetry relates spinning and non-spinning wave function coefficients
Used to derive the kinematic prefactor that captures the full WFC.

pith-pipeline@v0.9.0 · 5452 in / 1289 out tokens · 41373 ms · 2026-05-10T17:14:31.948533+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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