Stress Tensors and Casimir Energies in the AdS/CFT Correspondence

TL;DR

The paper investigates how to extract the full stress-energy tensor of the boundary CFT from bulk supergravity in the AdS/CFT correspondence, with a focus on Casimir energies on toroidal geometries. It develops and compares three methods—asymptotic (p-brane) geometries, Brown–York quasilocal energy, and a coordinate scheme that isolates boundary perturbations—and applies them to compute the CFT stress tensor in several AdS/CFT setups. A key result is the Casimir energy on AdS soliton backgrounds, which at strong coupling yields a negative energy density that matches the weak-coupling form up to a coupling-dependent factor (a 3/4 ratio), illustrating how the tensor structure persists across regimes but normalization changes. The discussion highlights technical issues (background subtraction vs counterterms), the role of singular bulk geometries, and directions for extending the analysis to more general torus identifications and duality structures.

Abstract

We discuss various approaches to extracting the full stress-energy tensor of the conformal field theory from the corresponding supergravity solutions, within the framework of the Maldacena conjecture. This provides a more refined probe of the AdS/CFT correspondence. We apply these techniques in considering the Casimir energy of the conformal field theory on a torus. It seems that either generically the corresponding supergravity solutions are singular (i.e., involve regions of large string-scale curvatures), or that they are largely insensitive to the boundary conditions of the CFT on the torus.