AdS/CFT correspondence, quasinormal modes, and thermal correlators in N=4 SYM

We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green's functions of ${\cal N=4}$ SU(N) SYM theory in the limit of large N and large 't Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. The latter result allows us to reconstruct the finite-temperature R-current correlator at strong coupling in the limit of zero spatial momentum. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory.