From AdS/CFT correspondence to hydrodynamics. II. Sound waves

As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Green’s functions of the stress-energy tensor in N = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole in the correlators corresponding to propagation of sound waves in the N = 4 SYM plasma. The retarded Green’s functions obtained from gravity do indeed exhibit this pole, with the correct values for the sound speed and the rate of attenuation.