Coupling constant dependence of the shear viscosity in supersymmetric Yang–Mills theory

Abstract

Gauge theory -gravity duality predicts that the shear viscosity of N = 4 supersymmetric SU(N c ) Yang-Mills plasma at temperature T in the limit of large N c and large 't Hooft coupling g 2 Y M N c is independent of the coupling and equals to πN 2 c T 3 /8. In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the α ′ -corrected low-energy effective action of type IIB string theory. We also find the correction to the ratio of shear viscosity to the volume entropy density (equal to 1/4π in the limit of infinite coupling). The correction to 1/4π scales as (g 2 Y M N c ) −3/2 with a positive coefficient.

Stringy effects in black hole decay

“…We find this result intriguing and we shall make some comments on it in the discussion at the end. We should point out that a similar calculation was done for a system of D3-branes wherein the viscosity/entropy ratio does change at subleading order [24].…”

Shear viscosity of CFT plasma at finite coupling

“…Specifically, we show that the full spectrum Gauge theory plasma transport analysis in [10][11][12] and in this letter are done in the the full ten dimensional type IIB supergravity including higher-derivative curvature corrections [19][20][21][22]. As a separate computation, we show that similar analysis done in lower dimensional higher-derivative effective action (obtained without proper KaluzaKlein reduction) could be misleading.…”

“…Much less is known about viscosity of gauge theory plasma at finite coupling: the shear viscosity of N = 4 supersymmetric Yang-Mills plasma at finite coupling was computed in [10][11][12][13] 1 . The difficulties of extending the analysis of [10][11][12][13] to other examples of gauge/string correspondence are both technical and conceptual.…”

“…Conceptually, the problem is that the full set of such O(α ′3 )-corrections is not known presently. Typically, in studies of black brane thermodynamics [16][17][18] and hydrodynamics [10][11][12][13] at O(α ′3 ) one takes into account only curvature corrections to type IIB supergravity [19][20][21][22]. What is known is that additional terms must be present [23][24][25] and that they might affect the hydrodynamics of dual gauge theory plasma.…”

“…What is known is that additional terms must be present [23][24][25] and that they might affect the hydrodynamics of dual gauge theory plasma. Thus, the available results [10,12] for the shear viscosity of N = 4 SYM plasma can receive further corrections from Ramond-Ramond fluxes in the dual string theory description. We emphasize though that such corrections will be additive (to leading order in α ′ ), and contribution of O(α ′3 ) terms due to fluxes can be computed on top of type IIB supergravity, excluding purely higher-derivative curvature corrections.…”