Shear viscosity at the Ising-nematic quantum critical point in two-dimensional metals

In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio (k(B)/h) eta/s, where. is the shear viscosity and s is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension d = 2 by an expansion below d = 5/2. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations:. scales in the same manner as a chiral conductivity, and the ratio eta/s diverges at low temperature (T) as T-2/z, where z is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.