Infrared divergences in the EPRL-FK Spin Foam model

TL;DR

This paper introduces an algorithm to estimate divergence degrees in Lorentzian EPRL-FK spin foam amplitudes, providing bounds and numerical validation for various models and diagrams, advancing understanding of divergences in quantum gravity.

Contribution

The paper presents a novel algorithm for estimating divergence degrees in EPRL-FK spin foam models, with numerical validation and application to different models and diagrams.

Findings

Self-energy divergence is higher than previous lower bounds.

Algorithm accurately estimates divergence in toy models.

BF theory divergences are confirmed as in literature.

Abstract

We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We argue that our upper bound must be close to the actual value, and explain what numerical improvements are needed to verify this numerically. For the self-energy, this turns out to be significantly more divergent than the lower bound estimate present in the literature. We support the validity of our algorithm using 3-stranded versions of the amplitudes (corresponding to a toy 3d model) for which our estimates are confirmed numerically. We also apply our methods to the simplified EPRLs model, finding a completely convergent behavior, and to BF theory, independently recovering the divergent estimates present in the literature.