Asymptotically anti-de Sitter spacetimes: Conserved quantities

Abhay Ashtekar, Das Saurya

Research output: Contribution to journalArticlepeer-review

233 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)L17-L30
JournalClassical and Quantum Gravity
Volume17
Issue number2
DOIs
StatePublished - Jan 21 2000

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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