On massive higher spins and gravity. I. Spin 5/2

TL;DR

This paper analyzes gravitational interactions of a massive spin-5/2 field in four dimensions, including partially massless and massless limits, using a gauge-invariant frame-like formalism with Stueckelberg-type extra fields. It employs the Fradkin–Vasiliev approach to classify and construct cubic vertices, distinguishing minimal couplings from necessary non-minimal terms and showing that at the unitary boundary $m^2 = 4\Lambda$ minimal interactions vanish leaving only non-minimal ones. The work provides explicit results for massive, partially massless, and massless spin-5/2 couplings, plus the massless spin-2 sector, and analyzes how curvature deformations and field redefinitions maintain gauge invariance. A companion paper extends these methods to the massive spin-3 field, illustrating the generality of the approach.

Abstract

In this paper, we continue our investigation of gravitational interactions for massive higher spins extending our previous work on massive spin 3/2 and spin 2 to massive spin 5/2, including partially massless and massless limits. We use the gauge invariant frame-like description for massive fields, both for general analysis of possible vertices and for constructing the minimal vertex (i.e. vertex containing standard minimal interactions and non-minimal interactions with a minimum number of derivatives). In particular, we show that there is a special point m^2 = 4Λ, which corresponds to the boundary of a unitary allowed region in dS_4, where minimal interactions disappear, leaving only non-minimal ones.

Figures (1)

• Figure 1: Unitary forbidden region $m^2 < 4\Lambda$ for massive spin 5/2