Charge algebra in Al(A)dSn spacetimes

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Lambda -BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

Automated summary

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions without further boundary conditions, resulting in finite expressions after removing divergences using holographic renormalization procedure. The charges associated with boundary diffeomorphisms are generally non-vanishing, non-integrable, and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions, with a field-dependent 2-cocycle present. The analysis is specialized to different boundary conditions, such as Dirichlet boundary conditions and leaky boundary conditions, leading to various results such as the Brown-Henneaux central extension and the Lambda-BMS asymptotic symmetry group. In the flat limit, the asymptotic symmetry group contracts to the BMS group in n dimensions.