, Volume 208, Issue 2, pp 413-428

A Stress Tensor for Anti-de Sitter Gravity

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Abstract:

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 AdS5, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S 3×R.

Received: 20 April 1999 / Accepted: 8 July 1999