content_image/369860.jpg content_image/369864.jpg
<img src='content_image/369860.jpg'>

## 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]: 

<img src='content_image/369864.jpg'>

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- 

