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 = epsilon(ij)partial derivative(i)A(j).