Asymptotically anti-de Sitter spacetimes: Conserved quantities

Asymptotically anti-de Sitter spacetimes are considered in a general dimension d ≥ 4. As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is the anti-de Sitter group (although there is an interesting subtlety if d = 4). Asymptotic field equations imply that, associated with each generator ξ of this group, there is a quantity Q_ξ which satisfies the expected 'balance equation' if there is a flux of physical matter fields across the boundary I at infinity and is absolutely conserved in the absence of this flux. Irrespective of the dimension d, all of these quantities vanish if the spacetime under considerations is (globally) anti-de Sitter, Furthermore, this result is required by a general covariance argument. However, it contradicts some of the recent findings based on the conjectured ADS/CFT duality. This and other features of our analysis suggest that, if a consistent dictionary between gravity and conformal field theories does exist in fully non-perturbative regimes, it would have to be more subtle than the one used currently.