Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
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DOI：
10.1103/physrevd.106.044005
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发表时间：
2021-10
影响因子：
5
通讯作者：
Muxin Han;Zichang Huang;Hongguang Liu;Dongxue Qu
中科院分区：
文献类型：
--
作者：
Muxin Han;Zichang Huang;Hongguang Liu;Dongxue Qu
本文主要研究四维自旋泡沫量子引力的半经典行为。长期以来，对于曲线几何是否存在于自旋泡沫振幅的半经典区域，人们一直存在困惑，即所谓的flatness问题。目前的工作解决了这一困惑。通过数值计算，我们从三角剖分上的大j洛伦兹恩格尔-佩雷拉-罗维利-利文(EPRL)自旋泡沫显式fi和弯曲的Regge几何。这些曲线几何形状具有较小的Deficit角，并且与振幅的复杂临界点有关。曲线几何形状对自旋泡沫振幅的主要贡献与e i i成正比，其中i是几何形状的Regge作用加上更高阶曲率的修正。结果是，在半经典区域，自旋泡沫的振幅在以e i i加权的Regge几何构型上减小为积分。作为副产品，我们的结果还提供了一种机制来缓解自旋泡沫模型中的余弦问题。我们的结果为支持自旋泡沫量子引力的半经典一致性提供了重要证据。
This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 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 from 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 e i I , where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by e i I in the semiclassical regime. As a byproduct, 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.