Causality of higher-spin interactions on the (A)dS lightcone, with application to the static patch

TL;DR

This paper develops a generalized lightcone formulation for 4d Higher-Spin Gravity in (A)dS, extending Metsaev's AdS lightcone to de Sitter by allowing bulk lightcones and non-orthogonal frames. It introduces a chiral field frame that simplifies the cubic vertices, analyzes causal properties of massless HS interactions, and uses these insights to formulate and compute static-patch scattering between the de Sitter horizons, both in coordinate space and in spinor-helicity momentum space. The work provides a coherent procedure to evolve initial horizon data to final horizon data at leading order in cubic interactions, including a concrete gravity-like example, and demonstrates conformal invariance for Yang–Mills–like vertices within the HS setting. These results offer a tractable bulk computation of HS observables in de Sitter space and build toward a fuller understanding of HS holography and causality in quantum gravity contexts.

Abstract

We study Higher-Spin Gravity in 4-dimensional (Anti-)de Sitter space, at leading order in the interactions (cubic vertices), in the AdS lightcone formalism developed by Metsaev. Using the vertices' chiral structure, we extend the formalism into a broader class of lightcone frames, which allows for lightcones of bulk points. This enables us to write the lightcone theory in de Sitter space, where only these more general frames are available. It also allows us to formulate and verify (for the first time!) some causal properties of massless higher-spin interactions, involving lightcone foliations that share a lightray. These causal properties serve to both motivate and enable the computation of "static-patch scattering amplitudes" - the evolution of fields between the two horizons of the maximal observable region in de Sitter space. We present a computation scheme for such "amplitudes" in coordinate space, and in momentum space with spinor-helicity variables.