Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD

Abstract

The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac operator shows a strong dependence on the chemical potential. The cancellations which make this possible also occur on the microscopic scale, where they can be investigated by means of a random matrix model. We show that they can be understood in terms of orthogonality properties of orthogonal polynomials. In the strong non-Hermiticity limit they are related to integrability properties of the spectral density. As a by-product we find exact analytical expressions for the partially quenched chiral condensate in the microscopic domain at nonzero chemical potential.