Fermionic fields of higher spin in de Sitter space

TL;DR

This work analyzes fermionic higher-spin fields on four-dimensional de Sitter space, centering on the massive and gauge Rarita–Schwinger field and tying their dynamics to $SO(4,1)$ unitary representations. It develops explicit Lorentzian BD mode functions, computes late-time two-point correlators, and formulates a Euclidean sphere path integral for both massive and gauge cases via Harish-Chandra characters, including edge contributions. The authors extend the discussion to general half-integer spins, discuss quantisation challenges due to imaginary masses, and propose a conformal operator basis that captures the late-time boundary structure, revealing a boundary CFT-like shadow transform perspective. They further speculate on a microscopic theory comprising an infinite tower of fermionic and bosonic higher-spin fields, and outline a Euclidean higher-spin program where the 4-sphere partition function can be expressed through conformal higher-spin data on a 3D boundary, with potential implications for dS holography and higher-spin gravity.

Abstract

We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their relation to the representation theory of $SO(4,1)$ is discussed. In Lorentzian signature, we study properties of the Bunch-Davies mode functions, and the late time structure of their two-point functions. For the Rarita-Schwinger gauge field, we consider a quantisation procedure based on the Minkowskian limit of the field operator. In Euclidean signature, the fields are placed on a four-sphere and the Euclidean path integral is computed at one-loop. The resulting Euclidean partition function is expressed in terms of unitary Lorentzian group characters with edge corrections. The unitary nature of the characters contrasts the lack of a conventional real action for the Rarita-Schwinger gauge field in de Sitter space. We speculate on the microscopic properties of a theory comprised of an infinite tower of interacting integer and half-integer gauge fields in de Sitter space. Along the way, we discuss a potentially interesting expression for the higher-spin path integral on the four-sphere.