Quantum gravity asymptotics from the SU(2) 15j symbol

TL;DR

This paper derives the asymptotic behavior of the SU(2) 15j symbol using coherent states, linking it to 4-simplex geometry and quantum gravity spin foam models.

Contribution

It provides a detailed asymptotic analysis of the SU(2) 15j symbol, connecting boundary data to 4D Euclidean geometry and quantum gravity models.

Findings

Asymptotic formula relates to Regge action of 4-simplex

Geometry of boundary data is characterized

Links to quantum gravity spin foam amplitudes

Abstract

The asymptotics of the SU(2) 15j symbol are obtained using coherent states for the boundary data. The geometry of all non-suppressed boundary data is given. For some boundary data, the resulting formula is interpreted in terms of the Regge action of the geometry of a 4-simplex in 4-dimensional Euclidean space. This asymptotic formula can be used to derive and extend the asymptotics of the spin foam amplitudes for quantum gravity models. The relation of the SU(2) Ooguri model to these quantum gravity models and their continuum Lagrangians is discussed.