标题： 对称随机张量网络的 Ryu-Takayanagi 公式 显示英文标题

标题： Ryu-Takayanagi Formula for Symmetric Random Tensor Networks

摘要： 我们考虑随机张量网络（RTN）的特殊情况，其中每个张量都带有规范对称性约束。 我们计算这类态的Rènyi熵，并在大键耦合强度下恢复了Ryu-Takayanagi（RT）公式。 这一结果首先为现有RTN的RT公式推导提供了一个有趣的全新扩展。 此外，这种RTN公式的扩展使其与（张量）群场理论（和自旋网络）直接相关联，从而为在背景无关量子引力背景下实现张量网络/几何对偶提供了新的工具，并为将量子引力工具引入张量网络研究提供了可能性。 显示英文摘要

摘要： We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.