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A stress tensor for anti-de Sitter gravity. (English) Zbl 0946.83013

Summary: We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global Ad \(S_5\), and show that it exactly matches the Casimir energy of the dual \({\mathcal N}=4\) super Yang-Mills theory on \(S^3\times \mathbb{R}\).

MSC:

83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
81T20 Quantum field theory on curved space or space-time backgrounds
83E50 Supergravity
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