A Stress Tensor for Anti-de Sitter Gravity

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.

Authors and Affiliations

1. Jefferson Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA.¶E-mail: vijayb@pauli.harvard.edu, , , , , , US

   Vijay Balasubramanian

2. Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA.¶E-mail: pkraus@theory.uchicago.edu, , , , , , US

   Per Kraus

Received: 20 April 1999 / Accepted: 8 July 1999

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