Shear Viscosity at Infinite Coupling: A Field Theory Calculation

Abstract

I derive an exact integral expression for the ratio of shear viscosity over entropy density $\frac{\eta }{s}$ 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 non-perturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, $\frac{\eta }{s}$ is evaluated numerically at all values of the coupling. For infinite coupling, I find $\frac{\eta }{s}\simeq 0.42(1)\times N$. I show that this strong coupling result for the viscosity is universal for a large class of interacting bosonic O(N) models.

6 pages, 1 figure plus supplemental material; v2: fixed typos and buggy code for (84) in v1, corrected eta/s values; v3: typo in (9) corrected, Fig.1 updated (no change in results)

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• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
• On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity
• Dissipative processes at the acoustic horizon
• Interacting CFTs for all couplings: Thermal versus Entanglement Entropy at Large $N$