LQG propagator from the new spin foams

TL;DR

This work derives a graviton-like propagator within Euclidean Loop Quantum Gravity by employing boundary amplitudes and coherent intertwiners for a semiclassical boundary state of a regular 4-simplex. Using the EPRL$_\gamma$/FK$_\gamma$ spin-foam dynamics, a vertex expansion at leading order and a large-spin stationary-phase analysis yield an explicit expression for the LQG propagator, separating it into a Regge-term and a novel $\gamma$-term from $SO(4)$ fluctuations. The leading propagator scales as $G_{nm}^{abcd} \sim (\gamma j_0)^3$ and reproduces the perturbative graviton tensor structure in the limit $\gamma\to 0$, $j_0\to\infty$ with $\gamma j_0$ fixed, given appropriate boundary-state parameters $\alpha_k$. These results validate the semiclassical limit of new spin foams at lowest order and provide a framework for comparing LQG with perturbative quantum gravity, while highlighting the need to generalize to multi-vertex configurations and bulk semiclassicality analyses.

Abstract

We compute metric correlations in loop quantum gravity with the dynamics defined by the new spin foam models. The analysis is done at the lowest order in a vertex expansion and at the leading order in a large spin expansion. The result is compared to the graviton propagator of perturbative quantum gravity.