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Universal Corner Symmetry and the Orbit Method for Gravity

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arxiv 2207.06441 v2 pith:FGUXB54A submitted 2022-07-13 hep-th gr-qcmath-phmath.MP

Luca Ciambelli , Robert G. Leigh This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords algebracornersuniversalsymmetryasymptoticcornerdistancefinite
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abstract

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.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields

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