Quasi-normal modes of warped black holes and warped AdS/CFT correspondence

TL;DR

This paper analytically computes the quasi-normal modes of warped AdS3 black holes, confirming their correspondence with dual CFT operators and supporting the warped AdS/CFT conjecture.

Contribution

It provides the first analytical calculation of quasi-normal modes for warped AdS3 black holes, clarifies the role of coordinate transformations, and supports the warped AdS/CFT correspondence.

Findings

Quasi-normal modes match CFT pole predictions after coordinate adjustments.

Computed conformal dimensions of dual boundary operators.

Results support the validity of warped AdS/CFT correspondence.

Abstract

We analytically calculate the quasi-normal modes of various perturbations of spacelike stretched and null warped $AdS_3$ black holes. From AdS/CFT correspondence, these quasi-normal modes are expected to appear as the poles in momentum space of retarded Green functions of dual operators in CFT at finite temperature. We find that this is indeed the case, after taking into account of the subtle identification of quantum numbers. The subtlety comes from the fact that only after appropriate coordinate transformation the asymptotic geometries of warped black holes are the same as the ones of warped $AdS_3$ spacetimes. We show that in general the quasi-normal modes are in good agreement with the prediction of the warped AdS/CFT correspondence, up to a constant factor. As a byproduct, we compute the conformal dimensions of boundary operators dual to the perturbations. Our result gives strong support to the conjectured warped AdS/CFT correspondence.