Perturbing a quantum black hole

TL;DR

This paper investigates the analytic structure of correlators in a quantum black hole model, revealing how quantum corrections influence quasi-normal modes, pole-skipping, and chaos indicators, thus differentiating between distinct quantum black hole states.

Contribution

It provides a detailed analysis of quantum corrections on correlator structures, quasi-normal modes, and chaos indicators in the qBTZ black hole, highlighting differences from classical models.

Findings

Quantum corrections alter the quasi-normal mode spectrum.

Pole-skipping points show complex temperature dependence due to quantum effects.

Quantum corrections lead to unique pole collision signatures in Green's functions.

Abstract

We analyze the analytic structure of correlators in the field theory dual to the quantum Ba\~{n}ados-Teitelboim-Zanelli (qBTZ) black hole, a braneworld model incorporating exact backreaction from quantum conformal matter. We first compute the quasi-normal mode (QNM) spectrum of operators with dimension $\Delta$ and spin $s=0,\pm 1/2$. The leading QNMs and their overtones display qualitatively different behavior depending on the branch of qBTZ solution, which corresponds to distinct CFT states: branch 1 is a conical singularity dressed with a horizon while branch 2 is a quantum-corrected BTZ black hole. Consequently, the relaxation of probe matter effectively differentiates the CFT states and identifies the corresponding bulk descriptions. We then turn to pole-skipping locations where Green's functions are not unique. At these points, frequency is proportional to temperature, but momentum exhibits complex temperature dependence due to quantum effects. Under the assumption that the pole-skipping point closest to the origin reflects quantum chaos, we infer the likely behavior of the quantum Lyapunov exponent and butterfly velocity in the dual theory. Finally, we examine pole collisions in complex momentum space, showing that quantum corrections imprint a unique signature on the analytic structure of the poles in retarded Green's functions, resulting in level-crossing phenomena that differ notably from the level-touching phenomena in the uncorrected BTZ geometry.