In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any “long-range” bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the “convex hull condition” of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and ’t Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman–Mandula theorem to discrete symmetries, and an improved explanation of the decay \(\pi ^0\rightarrow \gamma \gamma \) in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in \(d+1\) dimensions with horizon topology \({\mathbb {T}}^p\times {\mathbb {S}}^{d-p-1}\).

在本文中，我们使用AdS / CFT对应关系来细化，然后建立一组关于量子引力对称性的旧猜想。我们首先显示，在具有CFT对偶的体量子重力理论中，任何离散或连续的全局对称性都将导致该CFT不一致，因此AdS / CFT中不存在整体全局对称性。然后，我们认为，任何“远程”体积规的对称性都会导致边界CFT中的全局对称，其一致性要求存在体积动力学对象，这些物体会以体积规组的所有有限维不可约表示形式进行转换。我们主要假设所有内部对称组都是紧凑的，但是我们也对CFT给出了一个一般条件，我们希望它在相当广泛的范围内是正确的，这暗示了这一点。我们将所有这些结果扩展到更高形式的对称性的情况。最后，我们将最近提出的将弱重力猜想的新动机扩展到更一般的规范组，从而重现了Cheung和Remmen的“凸包状态”。我们将详细讨论的一个关键点是，精确定义块体和边界中的规范和整体对称性是什么意思。我们在组装必要工具时遇到的量子场论结果包括无Noether电流的连续全局对称性，关于自发对称破坏的新观点和't Hooft异常，这是一种新的约束级参数，在存在基本夸克，哈密顿量的情况下有效具有任意离散量规组的量规理论的表述，将Coleman–Mandula定理扩展到离散对称，\（\ pi ^ 0 \ rightarrow \ gamma \ gamma \）在粒子物理学的标准模型中。我们还描述了爱因斯坦方程的新黑洞的解决方案在\（d + 1 \）与地平线拓扑尺寸\（{\ mathbb【T}} ^ P \倍{\ mathbb {S}} ^ {DP-1} \ ）。