We show that driven two dimensional Bose systems cannot exhibit algebraic superfluid order unless the underlying microscopic system is strongly anisotropic. Our result implies, in particular, that recent apparent evidence for Bose condensation of exciton-polaritons in semiconductor quantum wells must be an intermediate scale crossover phenomenon, while the true long distance correlations fall off exponentially. We obtain these results through a mapping of the long-wavelength condensate dynamics onto the anisotropic Kardar-Parisi-Zhang equation.
