Edge modes of tetrad gravity: Unlike diffeomorphisms, all shifts are integrable

TL;DR

This paper introduces an improved, always integrable notion of internal tetrad shifts in 4D gravity, enabling a comprehensive analysis of corner symmetries and suggesting new avenues for understanding quantum gravity dynamics.

Contribution

It develops an integrable framework for tetrad shifts in 4D gravity, revealing a deformed corner symmetry algebra and proposing extended BF theory as a promising approach.

Findings

Corner symmetry algebra is a deformation of ISO(1,3)^S involving curvature

All tetrad shifts are shown to be integrable even with corners

Extended BF theory may better describe tetrad gravity dynamics

Abstract

We present an improved notion of internal tetrad shifts in 4 dimensions which is always integrable in the presence of corners. This allows us to study the fully extended corner symmetry algebra of gauge charges, which is a deformation of $ISO(1,3)^S$ involving spacetime curvature. We argue this implies corner noncommutativity of the spin connection $\omega$. The latter in particular hints that an extended BF theory might be a better way understand the dynamics of tetrad gravity. This result presents us with an integrable, complete set of edge modes for gravity in 4D, with potential ramifications for asymptotic symmetries and quantisation.