Stress Tensors and Casimir Energies in the AdS/CFT Correspondence

TL;DR

This paper explores methods to derive the stress-energy tensor of conformal field theories from supergravity solutions within the AdS/CFT framework, focusing on Casimir energies on a torus and highlighting issues with singularities and boundary condition sensitivities.

Contribution

It introduces refined techniques for extracting the stress-energy tensor from supergravity solutions in the AdS/CFT correspondence, applied to Casimir energy calculations on a torus.

Findings

Supergravity solutions are often singular or involve large string-scale curvatures.

These solutions are largely insensitive to boundary conditions of the CFT.

The methods provide a more detailed probe of the AdS/CFT correspondence.

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.