Communications in Mathematical Physics

, Volume 208, Issue 2, pp 413–428

A Stress Tensor for Anti-de Sitter Gravity

  • Vijay Balasubramanian
  • Per Kraus

DOI: 10.1007/s002200050764

Cite this article as:
Balasubramanian, V. & Kraus, P. Comm Math Phys (1999) 208: 413. doi:10.1007/s002200050764


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 S3×R.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Vijay Balasubramanian
    • 1
  • Per Kraus
    • 3
  1. 1.Jefferson Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA.¶E-mail: vijayb@pauli.harvard.eduUS
  2. 2.Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USAUS
  3. 3.Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA.¶E-mail: pkraus@theory.uchicago.eduUS