Isolated surfaces and symmetries of gravity

Abstract

Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and paying attention to the maximal such symmetry could have important consequences to further elucidate the quantization of gravity. After establishing an algebraic off-shell derivation of the maximal closed subalgebra of the full bulk diffeomorphisms in the presence of an isolated corner, we show how to geometrically describe the latter and its embedding in spacetime, without constraining the geometry away from the corner, such as by assuming a foliation. The analysis encompasses arbitrary embedded surfaces, of generic codimensions k. The resulting corner algebra Ak, calling S the embedded surface and M the bulk, is that of the group