The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

Abstract

The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the $(\otimes\vecΦ)^{s}$ and $\vecΦ\otimes(\otimes\vec\partial)^{n}\vecΦ$ operators in the 1/N^2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.