Analytical evaluation of cosmological correlation functions

TL;DR

This paper computes one-loop four-point functions in de Sitter space using a reformulated effective field theory approach, revealing new insights into the dual conformal field theory's structure and operator dimensions.

Contribution

It introduces a novel method to evaluate cosmological correlators via flat space Feynman integrals and derives anomalous dimensions and OPE coefficients in the dual CFT.

Findings

Derived anomalous dimensions and OPE coefficients for the dual CFT.

Identified degeneracy in anomalous dimensions across spins.

Expressed cosmological correlators in terms of single-valued multiple polylogarithms.

Abstract

Using the Schwinger-Keldysh-formalism, reformulated in arXiv:2108.01695 as an effective field theory in Euclidean anti-de Sitter, we evaluate the one-loop cosmological four-point function of a conformally coupled interacting scalar field in de Sitter. Recasting the Witten cosmological correlator as flat space Feynman integrals, we evaluate the one-loop cosmological four-point functions in de Sitter space in terms of single-valued multiple polylogarithms. From it we derive anomalous dimensions and OPE coefficients of the dual conformal field theory at space-like, future infinity. In particular, we find an interesting degeneracy in the anomalous dimensions relating operators of neighboring spins.