Pushing Further the Asymptotics of the 6j-symbol

TL;DR

This paper analytically investigates the next-to-leading order asymptotics of the 6j-symbol in spinfoam models for quantum gravity, providing insights into quantum corrections in gravitational correlations.

Contribution

It offers the first analytical computation of the next-to-leading order asymptotics of the 6j-symbol and validates results with numerical checks.

Findings

Analytical expression for next-to-leading order asymptotics

Validation of results through numerical calculations

Enhanced understanding of quantum corrections in 3d quantum gravity

Abstract

In the context of spinfoam models for quantum gravity, we investigate the asymptotical behavior of the 6j-symbol at next-to-leading order. We compute it analytically and check our results against numerical calculations. The 6j-symbol is the building block of the Ponzano-Regge amplitudes for 3d quantum gravity, and the present analysis is directly relevant to deriving the quantum corrections to gravitational correlations in the spinfoam formalism.