The Vasiliev Grassmannian

TL;DR

This paper derives a Grassmannian integral representation for the scalar four-point function in Vasiliev higher-spin gravity in de Sitter space, revealing a surprising similarity to string theory amplitudes.

Contribution

It introduces a novel Grassmannian integral formula for Vasiliev higher-spin correlators, connecting higher-spin gravity to string-like amplitude structures.

Findings

The correlator has a form similar to the Veneziano amplitude.

The Grassmannian integral matches momentum-space results.

Analysis of singularities and residues confirms the formula.

Abstract

We express the scalar four-point function of minimal Vasiliev higher-spin gravity in de Sitter space as an integral over the orthogonal Grassmannian OGr(4,8). The full crossing-symmetric Vasiliev Grassmannian correlator is given by $(S^2+T^2+U^2)/(STU)$, where $S$, $T$, $U$ are the Grassmannian Mandelstam variables. Remarkably, this has the same form as the field-theory limit of the Veneziano amplitude, despite arising from the opposite, tensionless limit of an infinite massless higher-spin tower. We verify the formula by evaluating the Grassmannian contour integral and matching it to the momentum-space result, and analyze its singularities and residues directly in Grassmannian space.