This review is devoted to the discussion of the parallel existing between fourdimensional gauge theories and twodimensional 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, lowenergy theorems and other nonperturbative 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 instantonbased method for calculating the exact GellMannLow function and bifermionic condensates is described. An analogue of this method has been previously used by us in fourdimensional YangMills 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 nonperturbative quantum vainstein dimensional novikov shifman sigmamodels   Customers who bought this item also bought: 