A Bohr-Sommerfeld Quantization Formula for Quasinormal Frequencies of AdS Black Holes

Abstract

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