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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 η/s in the high-temperature quantum critical regime T>>|μ| and find that this strongly coupled quantum fluid comes close to perfect fluidity η/s=\hbar/(4πk_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.