Instantons in the presence of a fixed density of massless fermions in two dimensions

We investigate the effects of a fixed finite density of massless fermions on the instantons of the Abelian Higgs model in two Euclidean dimensions. By using an appropriate path-integral formalism, we calculate the generating functional and analyze it by means of a graphical expansion, in which instantons appear as interaction vertices. We find that the fixed-fermion-density constraint introduces a chemical potential μ as a Lagrange multiplier and that this changes the fermion propagators in the expansion, so as to account for the chemical potential in the usual manner of many-body theory. That, in turn, leads to a μ dependence for the dynamically generated mass in the case of two flavors and, thus, changes the picture of chiral-symmetry breaking. We also find that the existence of the chemical potential imposes a cutoff on the instanton density, thereby providing a mechanism for instanton suppression, in the same way as the static electric color field used by Callan, Dashen, and Gross to derive a bag picture of hadrons from quantum chromodynamics