A Stress Tensor for Anti-de Sitter Gravity

1999/02/17 by Vijay Balasubramanian, Per Kraus · 1 voice · 2 citations
Physics and Astronomy · #gr-qc #hep-th

paper · pdf · doi:10.1007/s002200050764

published as Commun.Math.Phys. 208 (1999) 413-428 · 19 pages. added footnote, reference

arxiv published 1999/02/17 · arxiv created 1999/12/28 · arxiv updated 1999/12/28

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 N=4 super Yang-Mills theory on S³ x R.

Cited by

• Carrollian-holographic Derivation of BMS Flux-balance Laws
• Conformal Einstein equation and symplectic flux with a positive cosmological constant

Discussions

• For a theory of AdS gravity, because this theory contains boundary, Gibbons-Hawking-York Boundary term is needed to make the variation principle well-posed. Typically, we end up with a theory with act [stackexchange, 2 points]