A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes

TL;DR

This paper derives a Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, enabling analysis of boundary CFT relaxation times and quasiparticle properties at large scalar mass or momentum.

Contribution

It introduces a novel quantization formula for quasinormal modes in AdS black holes applicable at large scalar mass or momentum, linking bulk frequencies to boundary CFT dynamics.

Findings

Relaxation time inversely proportional to operator dimension and temperature.

Existence of long-lived quasiparticles with exponentially small decay rates on S^{d-1}.

Scaling of pole imaginary parts with momentum in large momentum limit.

Abstract

We derive a quantization formula of Bohr-Sommerfeld type for computing quasinormal frequencies for scalar perturbations in an AdS black hole in the limit of large scalar mass or spatial momentum. We then apply the formula to find poles in retarded Green functions of boundary CFTs on $R^{1,d-1}$ and $RxS^{d-1}$. We find that when the boundary theory is perturbed by an operator of dimension $\Delta>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over \Delta \pi T} << {1 \over \pi T}$. Turning on a large spatial momentum can significantly increase it. For a generic scalar operator in a CFT on $R^{1,d-1}$, there exists a sequence of poles near the lightcone whose imaginary part scales with momentum as $p^{-{d-2 \over d+2}}$ in the large momentum limit. For a CFT on a sphere $S^{d-1}$ we show that the theory possesses a large number of long-lived quasiparticles whose imaginary part is exponentially small in momentum.