A saddle-point finder and its application to the spin foam model

TL;DR

This paper presents a new method for locating complex saddle points in analytically continued actions, demonstrated on the EPRL spin foam model, aiding in understanding quantum gravity path integrals.

Contribution

Introduces a saddle-point finder applicable to any analytically continued action, with specific applications to the EPRL spin foam model.

Findings

Successfully identified complex saddle points in the EPRL model

Estimated contributions of saddle points to the partition function

Provided geometrical interpretations of saddle points

Abstract

We introduce a saddle-point finder that can find the complex saddle points for any analytically continued action. We showcase our saddle-point finder by two examples in the EPRL spin foam model: the single vertex case and the case of triangulation $\Delta_3$. In both cases, the complex saddle points are found, and each saddle point's contribution to the partition function is estimated. We also discuss the geometrical interpretation of each saddle point.