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, zeta1=zeta2=0, while the third one zeta3 is allowed to be nonzero.