标题： 树与CDT中的空间拓扑变化 显示英文标题

标题： Trees and spatial topology change in CDT

摘要： 广义因果动态三角剖分（广义CDT）是一个二维量子引力模型，在该模型中允许发生有限数量的空间拓扑变化。 我们通过四边形划分与树之间的双射关系在离散层面上求解该模型。 在连续极限（缩放极限）下，振幅被证明与已知公式一致，并得到了环传播子和两点函数的显式表达式。 从组合学的角度来看，广义CDT被证明是具有有限面数的平面图的缩放极限，我们确定了该平面图集合上的距离函数。 最后，利用与平面图的关系，阐明了某些连续圆柱振幅的神秘恒等式。 显示英文摘要

摘要： Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using bijections between quadrangulations and trees. In the continuum limit (scaling limit) the amplitudes are shown to agree with known formulas and explicit expressions are obtained for loop propagators and two-point functions. It is shown that from a combinatorial point of view generalized CDT can be viewed as the scaling limit of planar maps with a finite number of faces and we determine the distance function on this ensemble of planar maps. Finally, the relation with planar maps is used to illuminate a mysterious identity of certain continuum cylinder amplitudes.