Pushing the asymptotics of the6j-symbol further

Abstract

In the context of spin-foam models for quantum gravity, we investigate the asymptotical behavior of the ${6j}$-symbol at next-to-leading order. This gives the first quantum gravity correction to the (3d) Regge action. 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 spin-foam formalism.