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

TL;DR

This paper introduces a straightforward method for calculating anomalous dimensions of composite operators up to order 1/N^2, demonstrating its effectiveness through critical exponent computations in the nonlinear sigma model.

Contribution

A new simple scheme for calculating anomalous dimensions of composite operators up to 1/N^2 order is developed and validated in the nonlinear sigma model.

Findings

Effective computation of critical exponents for specific operators.

Simplifications due to conformal invariance are discussed.

Method proves efficient for 1/N^2 order calculations.

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 $(\otimes\vec\Phi)^{s}$ and $\vec\Phi\otimes(\otimes\vec\partial)^{n}\vec\Phi$ 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.