TY - JOUR
T1 - Asymptotically anti-de Sitter spacetimes
T2 - Conserved quantities
AU - Ashtekar, Abhay
AU - Saurya, Das
PY - 2000/1/21
Y1 - 2000/1/21
N2 - 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 Qξ 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.
AB - 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 Qξ 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.
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U2 - 10.1088/0264-9381/17/2/101
DO - 10.1088/0264-9381/17/2/101
M3 - Article
AN - SCOPUS:0034695292
SN - 0264-9381
VL - 17
SP - L17-L30
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 2
ER -