Asymptotic analysis of the Ponzano-Regge model for handlebodies

TL;DR

This paper derives an asymptotic formula for the Ponzano-Regge model amplitude on handlebodies, revealing connections to boundary triangulations, Regge action, and flexible immersions, verified numerically for large spins.

Contribution

It provides the first asymptotic analysis of the Ponzano-Regge model for handlebodies using coherent state techniques, linking boundary data to geometric immersions.

Findings

Asymptotic formula involves a sum over boundary immersions.

The formula is expressed as a cosine of the Regge action.

Numerical verification confirms the approximation for large spins.

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.