Towards the graviton from spinfoams: the 3d toy model

TL;DR

This paper investigates a 3D toy model within the spinfoam formalism to understand the 2-point function of linearized quantum gravity, revealing harmonic oscillator behavior and deviations at short scales.

Contribution

It demonstrates that the 3D spinfoam propagation kernel behaves like a harmonic oscillator in the semi-classical limit, providing insights into quantum gravity correlations.

Findings

Propagation kernel matches harmonic oscillator in the semi-classical limit

Reproduces expected 1/L behavior of the 2-point function

Identifies deviations at short scales

Abstract

Recently, a proposal has appeared for the extraction of the 2-point function of linearised quantum gravity, within the spinfoam formalism. This relies on the use of a boundary state, which introduces a semi-classical flat geometry on the boundary. In this paper, we investigate this proposal considering a toy model in the (Riemannian) 3d case, where the semi-classical limit is better understood. We show that in this limit the propagation kernel of the model is the one for the harmonic oscillator. This is at the origin of the expected 1/L behaviour of the 2-point function. Furthermore, we numerically study the short scales regime, where deviations from this behaviour occur.