三维量子引力中的跃迁振幅：着色Boulatov模型中的边界与全息
Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
AI总结：
本文研究三维黎曼量子引力着色Boulatov模型的跃迁振幅，通过修改张量模型生根过程将其写成拓扑展开，并证明2-球面边界振幅可因式分解，大N极限下主导阶为封闭3-球，为全息研究奠定基础。
摘要：
我们考虑三维黎曼量子引力着色单纯Boulatov模型中的跃迁振幅。首先，我们讨论具有非空边界的着色图的拓扑性质。利用对着色张量模型标准生根过程的修改，我们随后将跃迁振幅系统地写成拓扑展开。我们分析了最简单边界拓扑（即2-球面）的跃迁振幅，并证明它们可因式分解为一个完全由边界自旋网络态组合学给出的求和，且在大N极限下，其主导阶由表示封闭3-球的图给出。这是对着色Boulatov型GFT模型在拓扑场论和量子引力中全息性质的更详细研究的第一步。
英文摘要：
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.
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