Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method(Particles and Fields)

概要

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The three dimensional nonlinear sigma model is nonrenormalizable within the perturbative method. Using the β function in the nonperturbative Wilsonian renormalization group method, we argue that some N = 2 supersymmetric nonlinear σ models are renormalizable in three dimensions. When the target space is an Einstein-Kahler manifold with positive scalar curvature, such as CP^N 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 CP^N 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 β 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 CP^N model, and the symmetry is enhanced to SU(N + 1).
理論物理学刊行会の論文
2003-09-25