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

Understand

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.