Summing bulk quantum numbers with Monte Carlo in spin foam theories

TL;DR

This paper presents a Monte Carlo method to efficiently compute complex spin foam amplitudes in quantum gravity, revealing potential finiteness in the EPRL vertex renormalization amplitude.

Contribution

It introduces a uniform sampling Monte Carlo approach within the sl2cfoam-next framework to numerically evaluate spin foam amplitudes with many internal faces.

Findings

Monte Carlo sampling effectively approximates sums over internal quantum numbers.

The method reduces computational resources needed for large volume divergence calculations.

Numerical evidence suggests the EPRL vertex renormalization amplitude may be finite.

Abstract

We introduce a strategy to compute EPRL spin foam amplitudes with many internal faces numerically. We work with sl2cfoam-next, the state-of-the-art framework to numerically evaluate spin foam transition amplitudes. We find that uniform sampling Monte Carlo is exceptionally effective in approximating the sum over internal quantum numbers of a spin foam amplitude, considerably reducing the computational resources necessary. We apply it to compute large volume divergences of the theory and find surprising numerical evidence that the EPRL vertex renormalization amplitude is instead finite.