Spinors in (Anti-)de Sitter Space

TL;DR

This paper develops a formalism to relate fermionic correlators in de Sitter space to Euclidean anti-de Sitter space diagrams, providing new insights into fermion interactions and unitarity in curved spacetime.

Contribution

It adapts existing techniques to fermions in de Sitter space, establishing a spectral decomposition and connecting in-in correlators to Euclidean AdS Witten diagrams.

Findings

Relates fermionic correlators in de Sitter to Euclidean AdS diagrams.

Establishes a positive spectral decomposition for spinor Wightman functions.

Demonstrates implications of unitarity for fermionic correlators.

Abstract

We explore analytical aspects of correlators involving Dirac spinors in $d+1$- dimensional de Sitter space. Adapting the formalism of Sleight and Taronna, we show how to relate processes involving fermions in the in-in formalism to equivalent Witten diagrams in (complexified) Euclidean anti-de Sitter space. We exemplify the method for a fermion-exchange diagram. We establish a positive spectral decomposition over the principal series of the Wightman function of two spinors, showing the consequences of unitarity.