Addendum: EPRL/FK Asymptotics and the Flatness Problem

TL;DR

This paper refines previous calculations in spin foam models, deriving an alternative curvature constraint applicable to a wide range of boundary data, thereby resolving existing theoretical tensions.

Contribution

It removes an approximation in prior work to derive a more general and accurate curvature constraint in spin foam models, extending applicability to various boundary data and face amplitudes.

Findings

Derived an alternative curvature constraint without the previous approximation

Extended the result to most non-degenerate Regge-like boundary data

Resolved a tension in the theoretical literature on spin foam asymptotics

Abstract

We show that, when an approximation used in this prior work is removed, the resulting improved calculation yields an alternative derivation, in the particular case studied, of the accidental curvature constraint of Hellmann and Kaminski. The result is at the same time extended to apply to almost all non-degenerate Regge-like boundary data and a broad class of face amplitudes. This resolves a tension in the literature.