Two-phase model and the Johnson vacuum in one dimension

We discuss the relevant vacuum fluctuations in a two-phase model of the light baryons, in one dimension. It is shown that the limiting procedure in which the quark phase is shrunk to zero size is problematic within a naive chiral bag formulation. To circumvent these difficulties, a cutoffdependent chiral bag model is constructed, using Johnson's description of the vacuum state in two-dimensional QCD. The resulting picture is shown to interpolate continuously between bagged QCD2 and a sine-Gordon model. Pertinent conclusions for three dimensions are sketched.