3d QFT IR divergences as UV divergences in 4d Holographic Cosmology

TL;DR

This paper investigates IR divergences in a 3d toy model for 4d holographic cosmology, proposing a mass regularization approach that suggests IR finiteness and relates to UV finiteness in the dual 4d cosmological setting.

Contribution

It introduces a mass term preserving conformal structure to analyze IR divergences, providing evidence for IR finiteness beyond perturbation theory in holographic cosmology.

Findings

Computed 2- and 3-point functions at 2-loops showing IR behavior

Argued for IR finiteness beyond perturbation theory

Linked IR finiteness in 3d theory to UV finiteness in 4d cosmology

Abstract

In this paper we consider IR divergences in a 3d toy model field theory for 4d holographic cosmology, and we analyze them by introducing a mass term in a way that preserves a certain form of the generalized conformal structure. This allows us to compute 2- and 3-point functions at 2-loops and study their IR structure below the mass scale, from which we argue for a possible IR finiteness beyond perturbation theory, consistent with lattice results. In the holographically dual 4d cosmology, this corresponds to UV finiteness, i.e., the absence of cosmological singularities. The 3d IR field theory methods could be extended beyond this specific application.