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

TL;DR

This paper verifies the gauge/gravity duality by computing stress-energy tensor correlators in N=4 SYM at finite temperature, confirming the presence of sound wave poles with correct physical parameters.

Contribution

It provides a non-trivial check of the gauge/gravity duality by matching hydrodynamic predictions with gravity calculations for sound modes in a thermal plasma.

Findings

Retarded Green's functions show sound wave poles.

Sound speed and attenuation match hydrodynamic predictions.

Confirms gauge/gravity duality in non-supersymmetric context.

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.