CPN-1 models at a Lifshitz point

We consider CPN-1 models in d+1 dimensions around Lifshitz fixed points with dynamical critical exponent z, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the CPN-1 fields for all d=z. We demonstrate that, for z=d=2, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual CPN-1 models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has z=2, and an essentially singular dependence of the effective action on B=εij∂iAj.