On massive higher spins and gravity. II. Spin 3

TL;DR

This paper explores gravitational interactions of massive spin 3 particles in de Sitter space, extending previous work on higher spins, and identifies special mass points where minimal interactions vanish.

Contribution

It develops a gauge invariant frame-like formalism for massive spin 3 interactions, including massless and partially massless limits, and analyzes the behavior at a critical mass point.

Findings

Minimal interactions vanish at m^2=6Λ in dS_4.

Constructs gauge invariant vertices for massive spin 3.

Identifies special mass points affecting interaction structure.

Abstract

In this paper, we continue our investigation of gravitational interactions for massive higher spins, extending our recent work on massive spin 5/2 to massive spin 3, including its massless and partially massless limits. To construct the minimal gravitational interactions (i.e. vertexes containing both standard minimal interactions and non-minimal ones, which are necessary for any $s \ge 5/2$), we use a gauge invariant frame-like formalism. Similarly to the spin 5/2 case, there is a special point $m^2 = 6\Lambda$, which corresponds to a boundary of the unitary allowed region in $dS_4$, where minimal interactions disappear, leaving only the non-minimal ones.