Three and Four Point Functions of Stress Energy Tensors in D=3 for the Analysis of Cosmological Non-Gaussianities

TL;DR

This paper calculates 3- and 4-point stress energy tensor correlators in 3D free field theories, relevant for holographic cosmology, and compares results with existing holographic models, providing new insights into non-Gaussianities.

Contribution

It provides explicit computations of stress tensor correlators in 3D free theories and extends these results to non-Abelian gauge theories, aligning with recent holographic studies.

Findings

Correlators match holographic predictions for bispectra.

Explicit 4-point functions including contact terms are derived.

Results applicable to holographic models of cosmological non-Gaussianities.

Abstract

We compute the correlation functions of 3 and 4 stress energy tensors $(T)$ in D=3 in free field theories of scalars, abelian gauge fields, and fermions, which are relevant in the analysis of cosmological non-gaussianities. These correlators appear in the holographic expressions of the scalar and tensor perturbations derived for holographic cosmological models. The result is simply adapted to describe the leading contributions in the gauge coupling to the same correlators also for a non abelian SU(N) gauge theory. In the case of the bispectrum, our results are mapped and shown to be in full agreement with the corresponding expressions given in a recent holographic study by Bzowski, McFadden and Skenderis. In the 4-T case we present the completely traced amplitude plus all the contact terms. These are expected to appear in a fourth order extension of the holographic formulas for the 4-point functions of scalar metric perturbations.