Shear Viscosity of Strongly CoupledN=4Supersymmetric Yang-Mills Plasma

Abstract

Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity eta of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find eta = pi / 8N(2)T3. We conjecture that for finite 't Hooft coupling g(2)(YM)N the shear viscosity is eta = f(g(2)(YM)N)N2T3, where f(x) is a monotonic function that decreases from O(x(-2)ln(-1)(1/x)) at small x to pi/8 when x-->infinity.

What RHIC experiments and theory tell us about properties of quark–gluon plasma?

“…In particular, the viscosity to entropy ratio was found to be [19] η s = 1 4π (6) which is probably the smallest possible value, as it is obtained for an infinite coupling. One thing that became clear to us [21] is the meaning of the black hole.…”

“…That forced us to think hard Why is the Quark-Gluon Plasma at RHIC such an ideal fluid ? Important paper by Policastro, Son and Starinets [19] was a radical step in this direction.…”

Mesons in gauge/gravity duals

“…Amongst these is the famous ratio of shear viscosity to volume density of entropy which takes the value /4πk B [186]. This corresponds to the "fluid" with the lowest-known value of this ratio.…”

Drag force in a charged Script N = 4 SYM plasma

“…Policastro, Son and Starinets pioneered the study of hydrodynamic gauge theory properties using AdS/CFT [6,7]. In [6], these authors computed the shear viscosity η of strongly-coupled N =4 super-Yang-Mills (SYM) theory in 3 + 1 dimensions and at finite temperature.…”

“…Policastro, Son and Starinets pioneered the study of hydrodynamic gauge theory properties using AdS/CFT [6,7]. In [6], these authors computed the shear viscosity η of strongly-coupled N =4 super-Yang-Mills (SYM) theory in 3 + 1 dimensions and at finite temperature. They found that the ratio of shear viscosity to entropy density equals 1/4π, a result that was later argued to be universal, in the sense that it applies to any gauge theory described by a supergravity dual, in the limit of large 't Hooft coupling [8].…”