论文标题
3D量子重力中的过渡幅度：彩色Boulatov模型中的边界和全息图
Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
论文作者
论文摘要
我们考虑三维riemannian量子重力的彩色简单布拉托夫模型中的过渡幅度。首先，我们讨论具有非空边界的彩色图形拓扑的各个方面。然后，使用彩色张量模型的标准生根过程的修改，然后系统地编写过渡幅度作为拓扑扩展。我们分析了最简单的边界拓扑（2范围）的过渡幅度，并证明它们将其分为一个由边界旋转网络状态的组合设备完全给出的总和，并且领先顺序由代表大N极限的封闭3个球的图形给出。这是迈向对拓扑场理论和量子重力的彩色Boulatov型GFT模型的全息性质进行更详细研究的第一步。
We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity.
