Shear viscosity in weakly coupled ${\cal N} {=} 4$ Super Yang-Mills theory compared to QCD

Abstract

We compute the shear viscosity of weakly coupled N=4 supersymmetric Yang-Mills (SYM) theory. Our result for [eta/s], the viscosity to entropy-density ratio, is many times smaller than the corresponding weak-coupling result in QCD. This suggests that [eta/s] of QCD near the transition point is several times larger than the viscosity bound, [eta/s] >= 1/4 pi.

Figures (3)

• Figure 1: Shear viscosity to entropy density ratio $\eta/s$ in ${\cal N}{=}4$ supersymmetric Yang-Mills theory (SYM). The dotted curve is the weak coupling calculation pushed beyond its likely range of validity.
• Figure 2: $\eta/s$ for SYM theory and for QCD, scaled by the dominant $\lambda$ dependence and plotted as a function of $\lambda$. The value in SYM is dramatically smaller than in QCD.
• Figure 3: Leading-order $\eta/s$ for SYM and for QCD, scaled by $C_{\rm avg}\lambda m_{\rm D}^2/T^2$, which we argue in the text captures the dominant coupling dependence, as a function of $m_{\rm D}/T$.