Three dimensional nonlinear sigma models in the Wilsonian renormalization method

The three dimensional nonlinear sigma model is nonrenormalizable within the perturbative method. Using the beta function in the nonperturbative Wilsonian renormalization group method, we argue that some N = 2 supersymmetric nonlinear sigma models are renormalizable in three dimensions. When the target space is an Einstein-Kahler manifold with positive scalar curvature, such as CPN or Q(N), there are nontrivial ultraviolet (UV) fixed points, which can be used to define the nontrivial renormalized theory. If the target space has a negative scalar curvature, however, the theory has only an infrared Gaussian fixed point, and the meaningful continuum theory cannot be defined. We also construct a model that interpolates between the CPN and Q(N) models with two coupling constants. This model has two non-trivial UV fixed points that can be used to define a nontrivial renormalized theory. Finally, we construct a class of conformal field theories with SU(N) symmetry, defined at the fixed point of the nonperturbative beta function. These conformal field theories have a free parameter corresponding to the anomalous dimension of the scalar fields. If we choose a specific value of this parameter, we recover the conformal field theory defined at the UV fixed point of the CPN model, and the symmetry is enhanced to SU(N + 1).