Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion

TL;DR

This paper analyzes the behavior of light scalar fields in de Sitter space at next-to-leading order in 1/N, providing exact solutions for correlators and addressing infrared divergences through resummation techniques.

Contribution

It offers an exact analytical solution for the scalar field correlator at NLO in 1/N, including resummation of divergences and analysis of strongly coupled regimes.

Findings

Resummation of infrared divergences into power laws

Field strength and mass renormalization derived

Applicable to strongly coupled infrared theories

Abstract

We study the dynamics of light quantum scalar fields in de Sitter space on superhorizon scales. We compute the self-energy of an O(N) symmetric theory at next-to-leading order in a 1/N expansion in the regime of superhorizon momenta, and we obtain an exact analytical solution of the corresponding Dyson-Schwinger equations for the two-point correlator. This amounts to resumming the infinite series of nonlocal self-energy insertions, which typically generate spurious infrared and/or secular divergences. The potentially large de Sitter logarithms resum into well-behaved power laws from which we extract the field strength and mass renormalization. The nonperturbative 1/N expansion allows us to discuss the case of vanishing and negative tree-level square mass, which both correspond to strongly coupled effective theories in the infrared.