量子引力中非嵌入图的守恒拓扑缺陷
Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
摘要：
我们跟进以前的工作，发现常用的图形进化移动导致守恒量，可以表示在其嵌入空间中的图形的编织。我们研究了非嵌入图下三个不同的动力学规则集，并找到非平凡的守恒量，可以表示在对偶几何的拓扑缺陷。对于图对偶2维单纯复形，我们确定所有的保守量的演变。我们还表明预期的结果，图对偶的3维单纯复形。
英文摘要：
We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three distinct sets of dynamical rules and find non-trivial conserved quantities that can be expressed in terms of topological defects in the dual geometry. For graphs dual to 2-dimensional simplicial complexes we identify all the conserved quantities of the evolution. We also indicate expected results for graphs dual to 3-dimensional simplicial complexes.
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