A numerical study of the RG equation for the deformed $O(3)$ nonlinear sigma model

TL;DR

This paper numerically investigates the RG equations for a deformed $O(3)$ nonlinear sigma model, revealing that sausage solutions form an attracting manifold and testing theoretical associations at two-loop level.

Contribution

It provides a numerical analysis of the RG flow in a deformed $O(3)$ sigma model and tests theoretical predictions about the $SSM_{ u}$ field theory and scattering theory.

Findings

Sausage solutions attract in the $U(1)$-symmetric case at one-loop.

Numerical data supports the $SSM_{ u}$ and FST association at two-loop level.

The study advances understanding of RG flows in nonlinear sigma models.

Abstract

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two dimensional target space (deformation of the $O(3)$ sigma model). In particular, our analysis shows that the so-called sausages define an attracting manifold in the $U(1)$-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association put forward in Nucl. Phys., B406 (1993) 521 between the so-called $SSM_{\nu}$ field theory and a certain $U(1)$-symmetric, factorized scattering theory (FST).