2 4 6 8 10 0.2 0.4 0.6 0.8 1.0 f for attractive fermions PSfrag replacements f β k $^{2}$/ 2 m µ/T = 2 µ/T = 6 FIG. 3: Filling fraction f for attractive fermions at two different values of µ/T . VI. RATIO OF SHEAR VISCOSITY TO ENTROPY DENSITY The ratio of the shear viscosity η to the entropy density s has units of ℏ /k$_{B}$ in any dimension. A lower bound was conjectured for 3d relativistic systems[24]: η s ≥ ℏ 4 πk$_{B}$ (68) based on the AdS/CFT correspondence. The bound is saturated in certain strongly coupled supersymmetric gauge theories. It is therefore interesting to study this ratio for non-relativistic, strongly interacting systems, in 3 and lower dimensions, since it is unknown whether there really is a lower bound. This ratio was studied for 3 d unitary Fermi gases in [29–32]. The attractive fermion case is the most interesting and well-behaved case in our formalism, as will be evident in the subsequent sections, so we study the issue in this case first. Consider first a gas with a single species of particle of mass m . For a non- 23