Year: 2001
Type: article
Abstract: Using the anti--de Sitter/conformal field theory correspondence, we relate the shear viscosity $\ensuremath{\eta}$ of the finite-temperature $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$ 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 $\ensuremath{\eta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{\ensuremath{\pi}}{8}{N}^{2}{T}^{3}$. We conjecture that for finite 't Hooft coupling ${g}_{\mathrm{YM}}^{2}N$ the shear viscosity is $\ensuremath{\eta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}f({g}_{\mathrm{YM}}^{2}N){N}^{2}{T}^{3}$, where $f(x)$ is a monotonic function that decreases from $O({x}^{\ensuremath{-}2}{ln}^{\ensuremath{-}1}(1/x))$ at small $x$ to $\ensuremath{\pi}/8$ when $x\ensuremath{\rightarrow}\ensuremath{\infty}$.
Source: Physical Review Letters
Authors: G. Policastro, D. T. Son, A. O. Starinets
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2147579643