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

TL;DR

This paper investigates how replacing a BTZ black hole with a wormhole in AdS_3 space leads to a real spectrum of quasi-normal modes, suggesting a resolution to unitarity issues in AdS/CFT correspondence.

Contribution

It introduces a wormhole model in AdS_3 to produce real eigen-frequencies, addressing unitarity concerns in black-hole perturbations within the AdS/CFT framework.

Findings

Wormhole replaces black hole, yielding real eigen-frequencies.

Throat size is exponentially small in 1/G, indicating non-perturbative effects.

Spectrum of modes suggests unitarity preservation in the dual CFT.

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.