Shear Viscosity at Infinite Coupling: A Field Theory Calculation

TL;DR

This paper derives an exact integral expression for shear viscosity over entropy density in the large N O(N) model, providing a non-perturbative calculation at all couplings and revealing a universal value at infinite coupling.

Contribution

It introduces a non-perturbative field theory calculation of shear viscosity in the O(N) model at large N, including a universal value at infinite coupling.

Findings

At infinite coupling, η/s ≈ 0.42×N.

The calculation is valid for all coupling strengths.

The result is universal for a class of bosonic O(N) models.

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.