标题： 三维引力的微分同胚不变张量网络 显示英文标题

标题： Diffeomorphism invariant tensor networks for 3d gravity

摘要： 张量网络准备的状态具有与量子引力状态相似的许多特征。 然而，标准构造不是微分同构不变的，并且不支持非对易面积算子的代数。 最近，在具有有限或紧致规范群的拓扑场理论（TFT）的张量网络离散化中，解决了这两个问题的类似情况。 在这里，我们通过将规范群推广到离散或连续、紧致或非紧致的情况，将这项工作扩展到引力。 应用于$\text{SL}(2,\mathbb{R}) \times \text{SL}(2,\mathbb{R})$陈-西蒙斯理论，我们的构造可以解释为构建具有负宇宙常数的三维引力的状态。 我们的张量网络准备的状态满足陈-西蒙斯理论的约束条件。 在度量变量中，这意味着我们构造的状态满足惠勒-德威特方程和动量约束，因此是微分同构不变的。 显示英文摘要

摘要： Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of both problems were addressed in a tensor network discretization of topological field theories (TFT) with finite or compact gauge groups. Here, we extend this work towards gravity by generalizing to gauge groups that are discrete or continuous, compact or non-compact. Applied to $\text{SL}(2,\mathbb{R}) \times \text{SL}(2,\mathbb{R})$ Chern-Simons theory, our construction can be interpreted as building states of three dimensional gravity with a negative cosmological constant. Our tensor networks prepare states that satisfy the constraints of Chern-Simons theory. In metric variables, this implies that the states we construct satisfy the Wheeler-DeWitt equation and momentum constraints, and so are diffeomorphism invariant.