Lorentzian quantum gravity via Pachner moves: one-loop evaluation

• Published in: The journal of high energy physics 2023-09, Vol.2023 (9), p.69-50, Article 69
• Main Authors: Borissova, Johanna N., Dittrich, Bianca
• Format: Article
• Language: English
• Subjects: Calculus; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Lattice Models of Gravity; Models of Quantum Gravity; Obstructions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Triangulation
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2023)069

A bstract Lorentzian quantum gravity is believed to cure the pathologies encountered in Euclidean quantum gravity, such as the conformal factor problem. We show that this is the case for the Lorentzian Regge path integral expanded around a flat background. We illustrate how a subset of local changes of the triangulation, so-called Pachner moves, allow to isolate the indefinite nature of the gravitational action at the discrete level. The latter can be accounted for by oppositely chosen deformed contours of integration. Moreover, we construct a discretization-invariant local path integral measure for 3D Lorentzian Regge calculus and point out obstructions in defining such a measure in 4D. We see the work presented here as a first step towards establishing the existence of the non-perturbative Lorentzian path integral for Regge calculus and related frameworks such as spin foams. An extensive appendix provides an overview of Lorentzian Regge calculus, using the recently established concept of the complexified Regge action, and derives useful geometric formulae and identities needed in the main text.