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

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

1995-03-04

arxiv.org/abs/hep-th/9503026v2

Nucl.Phys. B443 (1995) 607-620

Physics

High Energy Physics

High Energy Physics - Theory

LaTex (RevTex style), 16 pages, 6 uuencoded figures. Minor technical changes.

Scientific paper

10.1016/0550-3213(95)00169-S

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).

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