| We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. The frequency dependent shear viscosity η(ω) exhibits a Drude-like transport peak and a power-law tail at large frequencies that is proportional to the Tan contact. The ratio η/s between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound ℏ/(4πkB) by a factor of about seven. |
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