Infrared divergences in the EPRL-FK Spin Foam model

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.

22 pages + 4 appendices, 8 figures. v2 match the published version

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• How-To compute EPRL spin foam amplitudes
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Spinfoams and high performance computing
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling