A Novel Holographic Framework Preserving Reflection Positivity in dS$_d$ Spacetime

Abstract

This manuscript introduces a novel holographic correspondence in $d$-dimensional de Sitter (dS$_d$) spacetime, connecting bulk dS$_d$ scalar unitary irreducible representations (UIRs) with their counterparts at the dS$_d$ boundary ${\cal{I}}^\pm$, all while preserving reflection positivity. The proposed approach, with potential applicability to diverse dS$_d$ UIRs, is rooted in the geometry of the complex dS$_d$ spacetime and leverages the inherent properties of the (global) dS$_d$ plane waves, as defined within their designated tube domains.