Vanishing bulk viscosities and conformal invariance of the unitary fermi gas

By requiring general-coordinate and conformal invariance of the hydrodynamic equations, we show that the unitary Fermi gas has zero bulk viscosity, zeta = 0, in the normal phase. In the superfluid phase, two of the bulk viscosities have to vanish, zeta(1) = zeta(2) = 0, while the third one zeta(3) is allowed to be nonzero.