Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

Han M, Huang Z, Liu H, Qu D (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Physical Review D American Physical Society

Book Volume: 106

Article Number: 044005

Journal Issue: 4

DOI: 10.1103/PhysRevD.106.044005

Abstract

This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in four dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries that contribute dominantly to the large-j Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to eiI, where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, in the semiclassical regime, the spinfoam amplitude reduces to an integral over Regge geometries weighted by eiI, where I is the Regge action plus corrections of higher order in curvature. As a by-product, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Authors with CRIS profile

Hongguang Liu Chair for Theoretical Physics III (Quantum Gravity)

Involved external institutions

Florida Atlantic University US United States (USA) (US) Fudan University / 复旦大学 CN China (CN)

How to cite

APA:

Han, M., Huang, Z., Liu, H., & Qu, D. (2022). Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity. Physical Review D, 106(4). https://dx.doi.org/10.1103/PhysRevD.106.044005

MLA:

Han, Muxin, et al. "Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity." Physical Review D 106.4 (2022).

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