Spikes and spines in 3D Lorentzian simplicial quantum gravity

TL;DR

This paper demonstrates that three-dimensional Lorentzian Quantum Regge Calculus can handle large bulk edges without infinities, unlike Euclidean approaches, and explores the complex configuration space including irregular light-cone structures.

Contribution

It shows that Lorentzian quantum gravity avoids infinities present in Euclidean models and reveals a richer configuration space with complex structures.

Findings

Partition function remains finite in Lorentzian case

Configuration space includes irregular light-cone structures

Imaginary terms and branch cuts in the Lorentzian path integral

Abstract

Simplicial approaches to quantum gravity such as Quantum Regge Calculus and Spin Foams include configurations where bulk edges can become arbitrarily large while keeping the lengths of the boundary edges small. Such configurations pose significant challenges in Euclidean Quantum Regge Calculus, as they lead to infinities for the partition function and length expectation values. Here we investigate such configurations in three-dimensional Lorentzian Quantum Regge Calculus, and find that the partition function and length expectation values remain finite. This shows that the Lorentzian approach can avoid a key issue of the Euclidean approach. We also find that the space of configurations, for which bulk edges can become very large, is much richer than in the Euclidean case. In particular, it includes configurations with irregular light-cone structures, which lead to imaginary terms in the Regge action and branch cuts along the Lorentzian path integral contour. Hence, to meaningfully define the Lorentzian Regge path integral, one needs to clarify how such configurations should be handled.