论文标题
通用角对称性和重力轨道方法
Universal Corner Symmetry and the Orbit Method for Gravity
论文作者
论文摘要
最近发现了一个通用的对称代数组织引力相空间。它对应于在拐角处变为物理的差异形态的子集 - 编辑 - $ 2 $表面支持Noether费用。它适用于有限距离和渐近角。在本文中，我们通过Coadhexhinexhight Orbit方法研究了该代数及其表示形式。我们表明，通用代数的通用轨道分为有限距离和渐近角对称性跨越的子孔，使得完整的通用对称代数产生了对歧管中角落的统一处理。然后，我们确定捕获这些代数属性在角上的几何结构，这是与主$ gl（2，\ mathbb {r}）\ ltimes \ ltimes \ mathbb {r}^2 $ bundle相关的Atiyah lie代数。这种结构暗示了一种新型的量子引力理论的存在，该理论将单位粘合这种几何结构，时空几何形状以半古典构型的形式出现。
A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners -- codimension-$2$ surfaces supporting Noether charges. It applies to both finite distance and asymptotic corners. In this paper, we study this algebra and its representations, via the coadjoint orbit method. We show that generic orbits of the universal algebra split into sub-orbits spanned by finite distance and asymptotic corner symmetries, such that the full universal symmetry algebra gives rise to a unified treatment of corners in a manifold. We then identify the geometric structure that captures these algebraic properties on corners, which is the Atiyah Lie algebroid associated to a principal $GL(2,\mathbb{R})\ltimes \mathbb{R}^2$-bundle. This structure is suggestive of the existence of a novel quantum gravitational theory which would unitarily glue such geometric structures, with spacetime geometries appearing as semi-classical configurations.
