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

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 $Δ>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over ΔπT} << {1 \over πT}$. 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.