Unitarity, quasi-normal modes and the AdS_3/CFT_2 correspondence

Abstract

In general, black-hole perturbations are governed by a discrete spectrum of complex eigen-frequencies (quasi-normal modes). This signals the breakdown of unitarity. In asymptotically AdS spaces, this is puzzling because the corresponding CFT is unitary. To address this issue in three dimensions, we replace the BTZ black hole by a wormhole, following a suggestion by Solodukhin [hep-th/0406130]. We solve the wave equation for a massive scalar field and find an equation for the poles of the propagator. This equation yields a rich spectrum of {\em real} eigen-frequencies. We show that the throat of the wormhole is $o(e^{-1/G})$, where $G$ is Newton's constant. Thus, the quantum effects which might produce the wormhole are non-perturbative.