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

TL;DR

This paper proposes a new holographic framework for de Sitter spacetime that maintains reflection positivity, linking bulk scalar representations to boundary data through complex geometry and dS plane waves.

Contribution

It introduces a novel holographic correspondence in dS spacetime that preserves reflection positivity and connects bulk and boundary representations using complex geometric methods.

Findings

Establishes a holographic map preserving reflection positivity in dS$_d$.

Connects bulk scalar UIRs with boundary counterparts at ${\

al}^\u00b0$ in de Sitter space.

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.