Isolated surfaces and symmetries of gravity

3d gravity in Bondi-Weyl gauge: charges, corners, and integrability

“…Moreover, the algebra which we have found here turns out to be an extension by Weyl translations of the algebra derived around finite null hypersurfaces whose radial position is kept fixed [23]. This could support the idea that the algebra which we have obtained here is maximal in the sense of [59] and of [23] when allowing for Weyl translations, but then begs the question of the status of the six charges found in [17,19].…”

“…• More generally, building up on the previous point, it would be interesting to understand what is the maximal number of finite and integrable charges which can be turned on in three-dimensional gravity (and of course also in higher-dimensional cases). It is noteworthy for example that an algebra similar to the Diff(C 2 ) + C ∞ (C 2 ) ⊕ C ∞ (C 2 ) found here (which becomes vir ⊕ vir ⊕ Heisenberg when represented in terms of the charges) has been found in [59], however in a very different context and without a realization in terms of charges. Moreover, the algebra which we have found here turns out to be an extension by Weyl translations of the algebra derived around finite null hypersurfaces whose radial position is kept fixed [23].…”

“…is reminiscent of the algebra found in [59], however in a very different context and without computing the charges. It would be interesting to study further the relationship between their construction and ours.…”

Extended corner symmetry, charge bracket and Einstein’s equations

“…This symmetry algebra has been shown, in a very recent work of Ciambelli and Leigh [11], to be the maximal closed subalgebra of the full bulk diffeomorphism group associated to isolated corners. From our perspective, this means that its representation theory should appear as a universal component of any quantization of gravity.…”

Gravitational edge modes, coadjoint orbits, and hydrodynamics

“…We have focused so far on the algebra of corner symmetries, which consist of transformations that fix the surface S. A necessary step for understanding the dynamics of the Casimirs would be to extend the algebraic picture described here to include transformations that move the surface. Several works [20,115,116] have proposed a larger symmetry group for codimension-2 surfaces in general relativity which includes surface translations. The particular algebra they found is diff(S) ⊕ sl(2, R) S ⊕ (R 2 ) S where the ⊕ denotes a semidirect sum in which diffeomorphisms act on sl(2, R) S ⊕ (R 2 ) S by Lie derivative, and sl(2, R) S acts on (R 2 ) S pointwise in the two-dimensional representation.…”