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=/(4πkB). Using a controlled large-N expansion, we show that already at the first nontrivial 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.