By adding a field-dependent Lorentz transformation to the naive tetrad shifts, the author constructs integrable improved shifts whose corner charge algebra is a curvature-deformed Poincaré algebra, and argues the spin connection becomes noncommutative on corners.
Cattaneo and Michele Schiavina
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Edge modes of tetrad gravity: Unlike diffeomorphisms, all shifts are integrable
By adding a field-dependent Lorentz transformation to the naive tetrad shifts, the author constructs integrable improved shifts whose corner charge algebra is a curvature-deformed Poincaré algebra, and argues the spin connection becomes noncommutative on corners.