A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model

Abstract

A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies of a universal shape function. This can be viewed as a 2-dimensional, but non-perturbative analogue of the KNO scaling in QCD. Promoted to a working hypothesis, it allows one to compute the two point functions at ``all'' energy or length scales. In addition, the values of two non-perturbative constants (needed for a parameter-free matching of the perturbative and the non-perturbative regime) are determined exactly.

arXiv comment9 Pages, Latex, 3 Postscript Figures

References in corpus (2)

• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

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• Quasi-asymptotic freedom in the two dimensional O(3) model
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Structure functions of 2d integrable asymptotically free models
• Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
• Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model
• Topological Susceptibility under Gradient Flow
• Comment on "Scaling Hypothesis for the Spectral Densities in the Nonlinear Sigma Model"