Radiative corrections to the Lorentzian EPRL spin foam propagator

TL;DR

This paper numerically investigates the divergence behavior of two-vertex diagrams in the Lorentzian EPRL spin foam model, identifying conditions under which these diagrams converge or diverge based on internal face count.

Contribution

It provides the first numerical analysis of divergences in Lorentzian EPRL spin foam diagrams, highlighting the role of internal face count in convergence.

Findings

Diagrams with fewer than six internal faces are convergent.

The divergence depends on the number of internal faces and the Immirzi parameter.

Numerical framework sl2cfoam-next effectively computes these amplitudes.

Abstract

We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk quantum numbers, fixed boundary data, and different Immirzi parameters, and find that for a class of two-vertex diagrams, those with fewer than six internal faces are convergent. The calculations are done with the numerical framework sl2cfoam-next.