Symmetries at Causal Boundaries in 2D and 3D Gravity

Abstract

We study 2d and 3d gravity theories on spacetimes with causal (timelike or null) codimension one boundaries while allowing for variations in the position of the boundary. We construct the corresponding solution phase space and specify boundary degrees freedom by analysing boundary (surface) charges labelling them. We discuss Y and W freedoms and change of slicing in the solution space. For D dimensional case we find D + 1 surface charges, which are generic functions over the causal boundary. We show that there exist solution space slicings in which the charges are integrable. For the 3d case there exists an integrable slicing where charge algebra takes the form of Heisenberg ⊕ A 3 where A 3 is two copies of Virasoro at Brown-Henneaux central charge for AdS 3 gravity and BMS 3 for the 3d flat space gravity.

Near horizon gravitational charges

“…In general, the integrable charge from Barnich-Troessaert prescription is different from the Noether charge. However it is conjectured in [20] and further verified in [67] that the two charges can be made identical by introducing a W term in the symplectic structure. We hope this W term and our 2-cocycle term can play a role in resolving the Kerr/CFT and Wald entropy discrepancy in high derivative gravities [68][69][70].…”