Asymptotic analysis of the Ponzano-Regge model for handlebodies

Abstract

Using the coherent state techniques developed for the analysis of the EPRL model we give the asymptotic formula for the Ponzano-Regge model amplitude for non-tardis triangulations of handlebodies in the limit of large boundary spins. The formula produces a sum over all possible immersions of the boundary triangulation and its value is given by the cosine of the Regge action evaluated on these. Furthermore the asymptotic scaling registers the existence of flexible immersions. We verify numerically that this formula approximates the 6j-symbol for large spins.