Shear viscosity of the normal phase of a unitary Fermi gas from the ε expansion

Using the epsilon-expansion technique, we compute eta/s, where. is the shear viscosity and s is the entropy density of the normal phase of unitary Fermi gas in d = 4 - epsilon dimensions to leading order (LO) in epsilon. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to epsilon(2), which is LO. The LO result is temperature independent with eta/s similar or equal to (0.11/e(2))((h) over bar /k(B)). The d = 3 prediction for eta/s exceeds the (h) over bar /4 pi k(B) bound by a factor of about 1.4.