  In bosonic gases at thermal equilibrium, an external quadratic drive can
induce a Bose-Einstein condensation described by the Ising transition, as a
consequence of the explicitly broken U(1) phase rotation symmetry down to
$\mathbb{Z}_2$. However, in physical realizations such as exciton-polaritons
and nonlinear photonic lattices, thermal equilibrium is lost and the state is
rather determined by a balance between losses and external drive. A fundamental
question is then how nonequilibrium fluctuations affect this transition. Here,
we show that in a two-dimensional driven-dissipative Bose system the Ising
phase is suppressed and replaced by a nonequilibrium phase featuring
Kardar-Parisi-Zhang (KPZ) physics. Its emergence is rooted in a U(1)-symmetry
restoration mechanism enabled by the strong fluctuations in reduced
dimensionality. Moreover, we show that the presence of the quadratic drive term
enhances the visibility of the KPZ scaling, compared to two-dimensional
U(1)-symmetric gases, where it has remained so far elusive.
