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 = h/(4 pi k(B)). 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.