Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Claudio Coriano, Luigi Delle Rose, Mirko Serino

TL;DR

This work computes the three-point and four-point functions of stress-energy tensors in D=3 free field theories (minimally and conformally coupled scalars, a chiral fermion, and a gauge field) to support holographic cosmology analyses of non-Gaussianities. It develops a consistent framework of Ward identities and helicity-based amplitudes, delivering explicit $TTT$ results for all sectors and a fully traced $TTTT$ amplitude assembled from box, triangle, and bubble topologies, with contact terms fully specified. The results include a non-Abelian extension via multiplicities and color factors, and are shown to map coherently to holographic formulas for cosmological perturbations, validating existing bispectrum mappings and laying groundwork for trispectrum extensions. Overall, the paper furnishes essential 3D boundary-theory building blocks that enable precise holographic predictions for scalar and tensor non-Gaussianities in cosmological models and guides future efforts to complete the fully uncontracted 4-point holographic trispectrum.

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.

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

TL;DR

This work computes the three-point and four-point functions of stress-energy tensors in D=3 free field theories (minimally and conformally coupled scalars, a chiral fermion, and a gauge field) to support holographic cosmology analyses of non-Gaussianities. It develops a consistent framework of Ward identities and helicity-based amplitudes, delivering explicit results for all sectors and a fully traced amplitude assembled from box, triangle, and bubble topologies, with contact terms fully specified. The results include a non-Abelian extension via multiplicities and color factors, and are shown to map coherently to holographic formulas for cosmological perturbations, validating existing bispectrum mappings and laying groundwork for trispectrum extensions. Overall, the paper furnishes essential 3D boundary-theory building blocks that enable precise holographic predictions for scalar and tensor non-Gaussianities in cosmological models and guides future efforts to complete the fully uncontracted 4-point holographic trispectrum.

Abstract

We compute the correlation functions of 3 and 4 stress energy tensors 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.

Paper Structure

This paper contains 23 sections, 113 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The search for non-gaussian fluctuations
  3. Domain-Wall/Cosmology correspondence and gauge/gravity duality
  4. Field theory realizations
  5. Conventions and the structure of the correlators
  6. Ward identities for the Green functions
  7. Computation of $TTT$
  8. Minimally coupled scalar
  9. Conformally coupled scalar
  10. Gauge field
  11. Chiral fermion
  12. Multiplicites in the non-abelian case
  13. Mapping of our result to the holographic one
  14. Computation of $TTTT$
  15. $TTTT$ for the minimally coupled scalar case
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Topologies appearing in the expansion of the $TTT$ correlator. Contributions involving coincident gravitons correspond to contact terms.
  • Figure 2: Topologies appearing in the expansion of the $4-T$ correlator $\textrm{BoxTop}$, $\textrm{TriTop}$, $\textrm{BubTop}_{22}$ and $\textrm{BubTop}_{13}$.
  • Figure 3: Tadpole topology for the TTTT correlator.