Quantum critical transport in the unitary Fermi gas

The thermodynamic and transport properties of the unitary Fermi gas at finite temperature T are governed by a quantum critical point at T=0 and zero density. We compute the universal shear viscosity to entropy ratio \eta/s in the high-temperature quantum critical regime T>>|\mu| and find that this strongly coupled quantum fluid comes close to perfect fluidity \eta/s=\hbar/(4\pi k_B). Using a controlled large-N expansion we show that already at the first non-trivial order the equation of state and the Tan contact density C agree well with the most recent experimental measurements and theoretical Luttinger-Ward and Bold Diagrammatic Monte Carlo calculations.