Analytic continuation of spinfoam models

Han M, Liu H (2022)

Publication Type: Journal article

Publication year: 2022


Book Volume: 105

Article Number: 024012

Journal Issue: 2

DOI: 10.1103/PhysRevD.105.024012


The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov spinfoam model and the Conrady-Hnybida timelike-surface extension can be expressed in the integral form ∫eS. This work studies the analytic continuation of the spinfoam action S to the complexification of the integration domain. Our work extends our knowledge from the real critical points well-studied in the spinfoam large-j asymptotics to general complex critical points of S analytic continued to the complex domain. The complex critical points satisfy critical equations of the analytic continued S. In the large-j regime, the complex critical points give subdominant contributions to the spinfoam amplitude when the real critical points are present. But the contributions from the complex critical points can become dominant when the real critical points are absent. Moreover, the contributions from the complex critical points cannot be neglected when the spins j are not large. In this paper, we classify the complex critical points of the spinfoam amplitude and find a subclass of complex critical points that can be interpreted as four-dimensional simplicial geometries. In particular, we identify the complex critical points corresponding to the Riemannian simplicial geometries although we start with the Lorentzian spinfoam model. The contribution from these complex critical points of Riemannian geometry to the spinfoam amplitude give e-SRegge in analogy with the Euclidean path integral, where SRegge is the Riemannian Regge action on the simplicial complex.

Authors with CRIS profile

Involved external institutions

How to cite


Han, M., & Liu, H. (2022). Analytic continuation of spinfoam models. Physical Review D, 105(2).


Han, Muxin, and Hongguang Liu. "Analytic continuation of spinfoam models." Physical Review D 105.2 (2022).

BibTeX: Download