Einstein gravity 3-point functions from conformal field theory

TL;DR

This paper demonstrates that in certain large N conformal field theories with sparse spectra, stress tensor three-point functions become universal and gravity-like, matching Einstein gravity predictions under causality constraints.

Contribution

It provides a direct CFT calculation showing the universality of stress tensor three-point functions approaching Einstein gravity form in holographic theories.

Findings

Stress tensor three-point functions become universal with increased spectral gap.

The unique consistent three-point structure matches Einstein gravity predictions.

The anomaly coefficients satisfy the relation a ≈ c, supporting holographic duality.

Abstract

We study stress tensor correlation functions in four-dimensional conformal field theories with large $N$ and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions $\langle TTT\rangle$, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy $a\approx c$ as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.