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

Muxin Han1,2, Zichang Huang3,4, Hongguang Liu2, and Dongxue Qu1,*

  • 1Department of Physics, Florida Atlantic University, 777 Glades Road, Boca Raton, Florida 33431-0991, USA
  • 2Institut für Quantengravitation, Universität Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen, Germany
  • 3Department of Physics, Center for Field Theory and Particle Physics, and Institute for Nano-electronic devices and Quantum computing, Fudan University, Shanghai 200433, China
  • 4State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China

  • *dqu2017@fau.edu
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Phys. Rev. D 106, 044005 – Published 10 August, 2022

DOI: https://doi.org/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.

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Outline

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Phys. Rev. D 106, 044005– Published 10 August, 2022
  • Received 22 November 2021
  • Accepted 19 July 2022
Article part of CHORUS
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