标题： 多不变量和整体复制对称性 显示英文标题

标题： Multi-invariants and Bulk Replica Symmetry

摘要： 本文中，我们分析了二维全息共形场论（CFT）真空态中多部分纠缠测度的体相复制对称性问题。 首先，我们定义了一类具有特定复制对称性的多部分局部幺正不变量，称为多不变量，该对称性在副本上自由且传递地作用。 然后，我们寻找一类测度，使得其对偶的体相几何也保留复制对称性。 如果我们要求体相几何在区域的一般配置下都保留复制对称性，那么我们将得到这个问题的最一般解。 通过用复制对称性对体相解进行orbifold操作，我们得到了一个具有锥形奇点网络的体相几何。 我们的方法清楚表明，存在无穷多个无穷大的多不变量子族，每个子族在全息态上的取值都相同。 从几何学角度来看，这些对应于模空间中某些点处涉及手柄体体积（可能具有不同亏格）的等式。 在某些情况下，我们通过CFT中的显式计算验证了体相计算的结果。 最后，我们讨论了将其推广到更高维度的可能性。 显示英文摘要

摘要： In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants, multi-invariants, with a given replica symmetry that acts freely and transitively on the replicas. We look for a subclass of measures such that the dual bulk geometry also preserves replica symmetry. We obtain the most general solution to this problem if we require the bulk to preserve replica symmetry for general configurations of the regions. Orbifolding the bulk solution with the replica symmetry gives us a bulk geometry with a network of conical singularities. Our approach makes it clear that there are infinitely many infinitely large families of multi-invariants such that each family evaluates identically on the holographic state. Geometrically, these are equalities involving volumes of handlebodies, possibly of different genus, at particular points in the moduli space. In certain cases, we check our bulk computation with an explicit calculation in CFT. Finally we comment on the generalization to higher dimension.