Fermionic fields of higher spin in de Sitter space

TL;DR

This paper investigates higher-spin fermionic fields, especially spin-3/2, in de Sitter space, analyzing their mode functions, two-point functions, and Euclidean path integrals, revealing insights into their representation theory and quantum properties.

Contribution

It provides a detailed analysis of higher-spin fermionic fields in de Sitter space, including quantization, mode functions, and Euclidean path integrals, with novel insights into their group-theoretic structure.

Findings

Mode functions exhibit specific late-time behaviors.

Euclidean partition functions are expressed via Lorentzian group characters.

The unitary nature of characters contrasts with the absence of a real action.

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.