  Fluids of exciton-polaritons, excitations of two dimensional quantum wells in
optical cavities, show collective phenomena akin to Bose condensation. However,
a fundamental difference from standard condensates stems from the finite
life-time of these excitations, which necessitate continuous driving to
maintain a steady state. A basic question is whether a two dimensional
condensate with long range algebraic correlations can exist under these
non-equilibrium conditions. Here we show that such driven two-dimensional Bose
systems cannot exhibit algebraic superfluid order except in low-symmetry,
anisotropic systems. Our result implies, in particular, that recent apparent
evidence for Bose condensation of exciton-polaritons 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.
