Two dimensional sigma-models: modelling non-perturbative effects in quantum chromodynamics

Two dimensional sigma-models: modelling non-perturbative effects in quantum chromodynamics This review is devoted to the discussion of the parallel existing between four-dimensional gauge theories and two-dimensional sigma models. We use sigma models as a laboratory allowing us to investigate such issues as the operator product expansion beyond perturbation theory, vacuum condensates, low-energy theorems and other non-perturbative aspects. All these questions are intensively discussed in the current literature, and we give a critical analysis of the situation. In particular, it is explained that, contrary to recent claims, one can define the operator product expansion beyond perturbation theory in a perfectly consistent way, with no ambiguities. The second part of the review represents a detailed discussion of the supersymmetric 0C) sigma model. After a simple description of the model we concentrate on instantons. The instanton-based method for calculating the exact Gell-Mann-Low function and bifermionic condensates is described. An analogue of this method has been previously used by us in four-dimensional Yang-Mills theories. Here we try to elucidate all aspects of the method in simplified conditions. The basic points are: (i) the instanton measure from purely classical analysis

Authors: Novikov V.A., Shifman M.A., Vainstein A.I.Pages: 69     Year: 1984

Tags: modelling effects chromodynamics non-perturbative quantum vainstein dimensional novikov shifman sigma-models
   

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