From AdS/CFT correspondence to hydrodynamics. II. Sound waves
G. Policastro, D. T. Son, A. O. Starinets
TL;DR
The paper demonstrates that finite-temperature N=4 SYM hydrodynamics, specifically sound modes, emerges from the gravity dual by computing retarded stress-energy correlators via near-horizon black brane geometry. Using linearized scalar perturbations and the GKPW prescription, the authors reproduce the hydrodynamic sound pole with $v_s=1/\sqrt{3}$ and attenuation $\omega = q/\sqrt{3} - i q^2/(6\pi T) + \cdots$, consistent with $\epsilon=3P$, $\zeta=0$, and $\eta/(\epsilon+P) = 1/(4\pi T)$. Ward identities and conformal constraints fix the infrared structure of correlators, and gravity exactly yields the expected pole structure and contact terms. This work strengthens the evidence for gauge/gravity duality at finite temperature and motivates exploration of hydrodynamic behavior in other brane backgrounds. The approach underscores the universality of hydrodynamic phenomena in holographic theories and their potential applicability to broader classes of strongly coupled plasmas.
Abstract
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.