| The quantum properties of supergravity theories on a four-dimensional Anti-de Sitter space background are investigated. It is shown that if supersymmetry is unbroken at the classical level then the one-loop vacuum is supersymmetric if and only if the one-loop vacuum energy vanishes. The unrenormalized vacuum energy is calculated and shown to be zero in an arbitrary theory if the classical background is supersymmetric, thereby showing that one-loop corrections always respect the supersymmetry of the vacuum.; Although the bare vacuum energy vanishes, the renormalized vacuum energy need not. The renormalized vacuum energy is shown to be determined by the infinite part of the one-loop effective action, and so is easily calculable. The resulting quantum correction to the background curvature is calculated and shown to vanish in any supersymmetric one-loop finite theory on AdS. In all cases calculated the quantum corrections, if nonzero, tend to reduce the background curvature. |
