usual sense of a zero of the beta function. The scattering length indeed diverges in this limit. The possibility of this kind of unitary limit in two dimensions has not been considered before in the literature. In the next section we describe the unitary limit in 1,2 and 3 dimensions and its relation to the renormalization group. In section III, we define the interesting scaling functions for the free energy and single-particle energies by normalizing with respect to free theories. In section IV we describe the unitary limit of the formalism in [20] in both two and three dimensions, where the integral equation becomes scale invariant. The d = 2 case is especially simple since the kernel reduces to a constant and the integral equation becomes algebraic. Analysis of these equations in 2 d is carried out for both infinitely repulsive or attractive fermions and bosons in sections V-VIII. The extension of our formalism to multiple species of possibly mixed bosonic and fermionic particles is considered in section IX. Kovtun et. al. conjectured that there is a universal lower bound to the ratio of the shear viscosity to the entropy density, where k$_{B}$ is Boltzmann’s constant[24]. This was based on the AdS/CFT correspon- dence for relativistic theories in 3 spatial dimensions, and the bound is saturated for certain supersymmetric gauge theories. Counterexamples to the η/s bound were suggested to be non-relativistic[24], however no known fluid violates the bound. It thus interesting to study this ratio for non-relativistic theories, and in particular for 2 d theories where no conjecture have been put forward. It has also been sug- gested that the gases in the unitary limit may represent the most perfect fluid, i.e. with the lowest value of η/s . For the spacetimes considered thus far for a non- relativistic AdS/CFT correspondence in 2d, the result found is that η/s is exactly 1 / 4 π [18, 19]. We analyze η/s for the attractive fermionic case as a function of µ/T 4 η/s ≥ ℏ 4 πk$_{B}$ (1)