Local flatness is a property shared by all the spin foam models. It ensures that the theory’s fundamental building blocks are flat by requiring locally-trivial parallel transport. In the context of simplicial Lorentzian spin foam theory, we show that local flatness is the main responsible for the emergence of geometry independently of the details of the spin foam model. We discuss the asymptotic analysis of the Engle-Pereira-Rovelli-Livine spin foam amplitudes in the large quantum number regime, highlighting the interplay with local flatness.

• Received 10 November 2022
• Accepted 22 February 2023

DOI:https://doi.org/10.1103/PhysRevD.107.066011