Geometry from local flatness in Lorentzian spin foam theories

TL;DR

This paper demonstrates that local flatness in Lorentzian spin foam models is crucial for the emergence of geometry, independent of specific model details, through asymptotic analysis of EPRL amplitudes.

Contribution

It reveals that local flatness drives geometric emergence in Lorentzian spin foam theories, regardless of the particular model implementation.

Findings

Local flatness ensures geometric emergence in spin foam models.

Asymptotic analysis links local flatness to EPRL amplitude behavior.

Geometry arises independently of model specifics due to local flatness.

Abstract

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 EPRL spin foam amplitudes in the large quantum number regime, highlighting the interplay with local flatness.