Tensors and Spinors in de Sitter Space

TL;DR

This paper develops a comprehensive formalism for constructing Wightman functions for tensors and spinors in de Sitter space, facilitating the study of arbitrary spin fields with applications in cosmology.

Contribution

It extends the ambient space formalism to include spinor and tensor fields in any dimension, providing explicit tools for analyzing fields of arbitrary spin in de Sitter space.

Findings

Explicit Wightman functions for tensors and spinors in de Sitter space.

General expressions for isometry actions on bulk fields.

Detailed derivation of spinor covariant derivatives in ambient space.

Abstract

We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ in a coordinate and index free formalism using a $d+2$ dimensional ambient space. We expand the embedding space formalism to cover spinor and tensor fields in any even or odd dimension. Our goal is to furnish a self-contained toolkit for the study of fields of arbitrary spin in de Sitter, with applications to cosmological perturbation theory. The construction for spinors is shown in extensive detail. Concise expressions for the action of isometry generators on generic bulk fields, the 2-point function of bulk spinors, and a derivation of the uplift of the spinorial covariant derivative are included.