de Sitter locality from conformal field theory

TL;DR

This paper explores how to reconstruct a scalar effective field theory in four-dimensional de Sitter space from boundary correlators, extending ideas from AdS/CFT to de Sitter backgrounds using crossing symmetry and Mellin space techniques.

Contribution

It introduces a method to derive de Sitter bulk locality from boundary CFT crossing symmetry, including novel constraints from anomalous dimensions and a Mellin space approach.

Findings

Reconstruction of de Sitter EFT from boundary correlators.

Derivation of constraints from anomalous dimensions.

Application of Mellin space and dispersion relations.

Abstract

An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how to reconstruct a conformally coupled scalar effective field theory (EFT) with higher derivative interactions in four-dimensional de Sitter space from its in-in correlators. The latter can be computed from a certain EFT in Euclidean Anti-de Sitter space involving two scalar fields, which we derive from crossing symmetry of boundary correlators along with two novel constraints arising from unmixing anomalous dimensions of degenerate operators and equating them in different OPE channels. To facilitate the analysis, we work in Mellin space and apply dispersion relations to extract anomalous dimensions more efficiently.