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

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.

Critical phenomena in SYM plasma

“…In this parametrization β 1 = β 2 = 1 for a conformal plasma with vanishing chemical potential [21]. Using (2.42), (2.43), (2.59), (3.14) and introducing 26) for the UV parameters (2.30), and 27) for the IR parameters (2.37), we find from (3.15)-(3.17)…”

A modulated shear to entropy ratio

“…The relation (1.1) has been observed to hold for a wide range of theories [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] with a general proof of its validity given in [19][20][21]. The proof of (1.1) relies on the system being in a thermally equilibrated isotropic and homogeneous configuration and on it being JHEP11(2014)019…”

Holographic quark gluon plasma with flavor

“…The corresponding result for the energy-momentum component correlator is obtained in an analogous way from the action and equations of motion already discussed in [29] . The final result is The real numbers C 1 , C 2 here are numerical values which are currently being checked.…”

“…In a series of papers [9,26,28,29,31,32,34,35] an identification of hydrodynamic modes with gravity objects was achieved leading to a detailed gravity description of the hydrodynamics in a strongly coupled fluid. Recently this framework has been extended to second order hydrodynamics [93,94,95,96].…”