Edge modes of gravity -- I: Corner potentials and charges

TL;DR

This paper explores how different formulations of gravity influence corner symmetries and representations, laying the groundwork for understanding quantum states of geometry through corner symmetry algebra.

Contribution

It demonstrates that various gravity formulations share the same bulk structure but differ at the corner, affecting symmetry representations and guiding quantum gravity research.

Findings

Different gravity formulations share bulk symplectic structure.

Corner symmetries vary depending on the formulation.

Framework for analyzing quantum geometry states based on corner symmetries.

Abstract

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a "treasure map" revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [2], and tackle the quantization in [3].