A Stress Tensor for Anti-de Sitter Gravity

TL;DR

This paper introduces a new, unambiguous method for computing the boundary stress tensor in asymptotically anti-de Sitter spaces, aligning with AdS/CFT predictions and reproducing known anomalies and energies.

Contribution

It presents a novel procedure for calculating the boundary stress tensor in AdS gravity that resolves previous ambiguities and matches dual CFT expectations.

Findings

Correctly reproduces masses and angular momenta of spacetimes.

Recovers conformal anomalies in 2D and 4D.

Matches Casimir energy of dual N=4 super Yang-Mills theory.

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 AdS_5, and show that it exactly matches the Casimir energy of the dual N=4 super Yang-Mills theory on S^3 x R.