Abstract
I derive an exact integral expression for the ratio of shear viscosity over entropy density η/s for the massless (critical) O(N) model at large N with quartic interactions. The calculation is set up and performed entirely from the field theory side using a nonperturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, η/s is evaluated numerically at all values of the coupling. For infinite coupling, I find (η/s)≃0.42(1)×N. I show that this strong coupling result for the viscosity is universal for a large class of interacting bosonic O(N) models.
Highlights
Experimental measurements of momentum anisotropies in heavy-ion collisions together with hydrodynamic modeling constrain the value of shear viscosity in QCD to ðη=sÞ ≲ 0.2 [1,2,3,4,5]
OðNÞ vector model with quartic interactions in 2 þ 1 dimensions in the large N limit, which exists for all values of the coupling
Including thermal fluctuations in the fluid dynamic calculations leads to a long-time tail contribution for d 1⁄4 3 of the form GRðω; k 1⁄4 0Þ ∝ 1⁄2iωT2=ðη=sÞ ln ω
Summary
Experimental measurements of momentum anisotropies in heavy-ion collisions together with hydrodynamic modeling constrain the value of shear viscosity in QCD to ðη=sÞ ≲ 0.2 [1,2,3,4,5] This numerical value happens to be not too dissimilar from the result ðη=sÞ 1⁄4 ð1=4πÞ ≃ 0.08 found for the conjectured strong-coupling limit of another gauge theory, N 1⁄4 4 supersymmetric Yang-Mills theory, in the large N limit [6,7,8]. OðNÞ vector model with quartic interactions in 2 þ 1 dimensions in the large N limit, which exists for all values of the coupling The choice of this theory is motivated by the fact that the entropy density s is known for all couplings [16] and that an efficient resummation scheme that captures all relevant contributions to the shear viscosity at large N is known [17,18].
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