Quantum-corrected anti-de Sitter space-time

Abstract

We study the back-reaction of a quantum scalar field on anti-de Sitter (AdS) space-time. The renormalized expectation value of the stress-energy tensor operator for a massless, conformally-coupled quantum scalar field on global AdS space-time in four space-time dimensions acts as a source term on the right-hand-side of the Einstein equations for the quantum-corrected metric. We solve the quantum-corrected Einstein equations numerically and find deviations from pure AdS which increase as the temperature of the quantum scalar field state increases. We interpret these quantum-corrected metrics as asymptotically-AdS solitons, and study the mass of these solitons as a function of the temperature of the quantum scalar field.

19 pages, 11 figures, minor changes, accepted for publication in Physical Review D