Gell-mann-low function of the chiral model on the homogeneous berger space

Abstract

The asymptotic freedon of two-dimensional nonlinear sigma models (chiral models) is one of the most important properties on which the analogy between 2d sigma models and 4d gauge theories is based. For the two-dimensional nonlinear sigma model on the homogeneous space Sp(2)/SU(2) (Berger manifold) the method of sectional curvatures is used to find the Gell-Mann-Low beta function in the single-loop approximation. The result indicates that the model is an asymptotically free renormalizable nonlinear model.