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Prog. Theor. Phys. Vol. 110 No. 3 (2003) pp. 563-578

Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method

Kiyoshi Higashijima^* and Etsuko Itou^**

Department of Physics, Graduate School of Science, Osaka University,
Toyonaka 560-0043, Japan

(Received April 30, 2003)

Abstract:

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-Kähler 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).

URL : http://ptp.ipap.jp/link?PTP/110/563/
DOI : 10.1143/PTP.110.563

^* E-mail: higashij@phys.sci.osaka-u.ac.jp
^** E-mail: itou@het.phys.sci.osaka-u.ac.jp

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 117 No. 6 (2007) pp. 1139-1156 :

   Three Dimensional Conformal Sigma Models

   Takeshi Higashi, Kiyoshi Higashijima and Etsuko Itou

2. Progress of Theoretical Physics Supplement No.164 (2006) pp. 103-108 :

   Wilsonian Renormalization Approach to Nonlinear Sigma Models

   Takeshi Higashi, Kiyoshi Higashijima and Etsuko Itou

3. Progress of Theoretical Physics Supplement No.181 (2009) pp. 1-166 :

   Realization of Symmetry in the ERG Approach to Quantum Field Theory

   Yuji Igarashi, Katsumi Itoh and Hidenori Sonoda

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