Balasubramanian, Vijay; Kraus, Per A stress tensor for anti-de Sitter gravity. (English) Zbl 0946.83013 Commun. Math. Phys. 208, No. 2, 413-428 (1999). 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 \(S^3\times \mathbb{R}\). Cited in 590 Documents 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 Keywords:asymptotically anti-de Sitter space; quantum conformal field theory; super Yang-Mills theory PDFBibTeX XMLCite \textit{V. Balasubramanian} and \textit{P. Kraus}, Commun. Math. Phys. 208, No. 2, 413--428 (1999; Zbl 0946.83013) Full Text: DOI arXiv