Revisiting zero modes and cluster decomposition at the late-time boundary of de Sitter

TL;DR

This paper analyzes how different representations of de Sitter's isometry group affect locality and cluster decomposition, revealing that matter fields respect these properties while gauge fields do not, especially in late-time behavior.

Contribution

It systematically compares the late-time two-point functions of principal and discrete series representations in de Sitter, clarifying their roles in locality and cluster decomposition.

Findings

Matter fields respect cluster decomposition at late times.

Gauge fields do not respect cluster decomposition.

Principal series captures matter fields, discrete series captures gauge fields.

Abstract

We revisit the literature on locality on de Sitter with the goal to organize the main results with respect to the representation theory of the isometry group of four dimensional de Sitter. We make use of the late-time behavior of two-point functions of principal and discrete series representation, both in physical and in field space and compare the role of the zero modes. Our overall conclusion is that when it comes to locality on de Sitter, analyzed in terms of cluster decomposition, the principal series representation that capture matter fields and discrete series representations that capture gauge fields show different behavior. Focusing on scalars as a first analysis, matter fields show explicit signs of respecting cluster decomposition while gauge fields do not.