A numerical study of the RG equation for the deformed O(3) nonlinear sigma model |
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| Affiliation: | 1. Dipartimento di Fisica, University di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy;2. Dipartimento di Fisica, Universita di Parma and INFN, Gruppo Collegato di Parma, Wale delle Scienze, 43100 Parma, Italy;1. Nikhef, Theory Group, Science Park 105, NL-1098 XG Amsterdam, the Netherlands;2. Institute of Physics, Laboratory for Particle Physics and Cosmology, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;1. ICRANet, Piazzale della Repubblica, 10, 65122, Pescara, Italy;2. Physics Department, University of Rome La Sapienza, Rome, Italy;3. INFN, Sezione di Perugia, Perugia, Italy;4. ICTP-AP, University of Chinese Academy of Sciences, Beijing, China |
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| 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) σ-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 (Fateev, Onofri and ALB. Zamolodchikov, Nucl. Phys. B 406 (1993) 521) between the so-called SSMη field theory and a certain U(1)-symmetric, factorized scattering theory (FST). |
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