Spinfoams and high performance computing

TL;DR

This paper reviews numerical methods and high-performance computing techniques for calculating spinfoam amplitudes, highlighting advances in algorithms, applications, and evidence for resolving key theoretical issues.

Contribution

It introduces and compares multiple computational frameworks for spinfoam theory, including the state-of-the-art library and alternative integration approaches.

Findings

Efficient computation of EPRL spin foam amplitudes using sl2cfoam-next.

Numerical evidence supporting the resolution of the flatness problem.

Estimation of observable expectation values via Lefschetz thimble and MCMC methods.

Abstract

Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to efficiently compute EPRL spin foam amplitudes based on the booster decomposition. We also review two alternative approaches based on the integration representation of the spinfoam amplitude: Firstly, the numerical computations of the complex critical points discover the curved geometries from the spinfoam amplitude and provides important evidence of resolving the flatness problem in the spinfoam theory. Lastly, we review the numerical estimation of observable expectation values based on the Lefschetz thimble and Markov-Chain Monte Carlo method, with the EPRL spinfoam propagator as an example.