Electrodynamic duality and vortex unbinding in driven-dissipative condensates

We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of nonlinear electrodynamics coupled to charges. Using the dual theory, we derive renormalization group equations that describe vortex unbinding in these media. When the nonequilibirum drive is turned off, the KPZ nonlinearity lambda vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with nonlinearity lambda > 0 vortices always unbind, even if the same system with lambda = 0 is superfluid. We predict the finite-size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition.