论文标题
准本地3D量子重力：精确的振幅和全息图
Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
论文作者
论文摘要
本论文致力于研究3D时空病例中量子重力中的准本地边界。这项研究扎根于全息原理，该原理猜测几何形状和时空区域的动态可以通过生活在该给定区域边界上的理论完全描述。该原理研究最多的案例是ADS/CFT对应关系，其中渐近广告空间的量子波动是通过居住在Virasoro组下的空间无穷大的保形场理论来描述的。本文中应用的哲学与广告/CFT案例不同。我专注于准本地全息图，即在有限距离的边界的时空界区域。目的是阐明ponzano-Regge模型所描述的量子重力中的块状结构关系，并通过离散路径积分定义了3D重力的模型。 我介绍了具有2D边界状态的圆环上的ponzano-Regge振幅的第一个扰动和精确计算。在以2D边界状态表示3D振幅的一般框架后，我考虑了2D圆环情况，并在研究BTZ黑洞的热力学研究中应用。首先，在半古典制度中，一个连贯的自旋网络状态描述了2D边界。固定相的近似允许在渐近极限中恢复3D量子重力的通常振幅，作为BMS组渐近平坦重力对称性的特征。然后，我引入了一种新型的连贯边界状态，该状态允许对3D量子重力的振幅进行精确评估。我获得了BMS字符的复杂正规化。该精确计算的可能性表明存在（准）综合结构，该结构与3D量子重力的对称性具有2D有限边界。
This thesis is dedicated to the study of quasi-local boundary in quantum gravity in the 3D space-time case. This research takes root in the holographic principle, which conjectures that the geometry and the dynamic of a space-time region can be entirely described by a theory living on the boundary of this given region. The most studied case of this principle is the AdS/CFT correspondence, where the quantum fluctuations of an asymptotically AdS space are described by a conformal field theory living at spatial infinity, invariant under the Virasoro group. The philosophy applied in this thesis differs from the AdS/CFT case. I focus on the case of quasi-local holography, i.e. for a bounded region of space-time with a boundary at a finite distance. The objective is to clarify the bulk-boundary relation in quantum gravity described by the Ponzano-Regge model, defining a model for 3D gravity via a discrete path integral. I present the first perturbative and exact computations of the Ponzano-Regge amplitude on a torus with a 2D boundary state. After the presentation of the general framework for the 3D amplitude in terms of the 2D boundary state, I consider the 2D torus case, with application in the study of the thermodynamics of the BTZ black hole. First, the 2D boundary is described by a coherent spin network state in the semi-classical regime. The stationary phase approximation allows to recover in the asymptotic limit the usual amplitude for 3D quantum gravity as the character of the symmetry of asymptotically flat gravity, the BMS group. Then I introduce a new type of coherent boundary state, which allows an exact evaluation of the amplitude for 3D quantum gravity. I obtain a complex regularization of the BMS character. The possibility of this exact computation suggests the existence of a (quasi)-integrable structure, linked to the symmetries of 3D quantum gravity with 2D finite boundary.
