标题： ADM超曲面上的全局转换对称性：迈向新兴引力 显示英文标题

标题： Global shift symmetry on an ADM hypersurface: Toward emergent gravity

摘要： 广义对称性及其自发破缺作为约束多体纠缠结构的基本概念，使我们能够表征物质的量子相以及涌现的集体激发。 例如，涌现的光子可以通过自发的一形式对称性破缺来理解，这种破缺源于紫外微观自由度之间的长程纠缠结构。 在这项研究中，我们表明类似的机制也可能产生“涌现的引力”，这里使用引号是为了强调与通常的引力子相比，受对称性约束的引力子表现出非常规性质。 由于麦克斯韦理论中的电一形式对称性表现为U(1)规范场的空间分量的全局平移对称性，由电场生成，我们证明了阿诺德-德瑟-米斯纳（ADM）度规在空间超曲面上的常数平移可以被视为一种全局对称性，由ADM正则动量生成。 通过从作用量的变化中推导出矢量型守恒荷，我们构建了一个平移对称算符。 考虑到维克旋转，我们证明了引力威尔逊圈在这种平移对称算符的作用下带电，从而确认了ADM超曲面上存在广义的全局对称性。 基于Ward恒等式，我们表明这种全局平移对称性的自发破缺可能会在超曲面边界处产生一个非传播的无质量对称规范场。 显示英文摘要

摘要： Generalized symmetries and their spontaneous breakdown serve as the fundamental concept to constrain the many-body entanglement structure, which allows us to characterize quantum phases of matter and emergent collective excitations. For example, emergent photons may be understood by spontaneous 1-form symmetry breaking, which results from a long-ranged entanglement structure between UV microscopic degrees of freedom. In this study, we show that emergent ``gravity" may also arise in a similar fashion, where quotes have been used to emphasize that the symmetry-constrained gravitons show unconventional properties compared to usual gravitons. As the electric 1-form symmetry in Maxwell theory is realized as a global shift symmetry of the spatial component of the U(1) gauge field, generated by the electric field, we demonstrate that a constant shift of the Arnowitt-Deser-Misner (ADM) metric on the spatial hypersurface can be viewed as a global symmetry, generated by the ADM canonical momentum. Deriving a vector-type conserved charge from the variation of action, we construct a shift symmetry operator. Considering a Wick rotation, we demonstrate that a gravitational Wilson loop is charged under the action of this shift symmetry operator, which thus confirms the existence of a generalized global symmetry on the ADM hypersurface. Based on the Ward identity, we show that the spontaneous breaking of this global shift symmetry may give rise to a nonpropagating massless symmetric gauge field at the boundary of the hypersurface.