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 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.