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

TL;DR

This paper investigates the behavior of the chiral condensate in QCD at nonzero chemical potential within the microscopic limit, revealing its independence from chemical potential and providing exact analytical expressions using random matrix models.

Contribution

It demonstrates the independence of the chiral condensate from chemical potential in the microscopic limit and derives exact analytical formulas using orthogonal polynomials and random matrix theory.

Findings

Chiral condensate remains unaffected by chemical potential at microscopic scale.

Derived exact formulas for the partially quenched chiral condensate.

Linked spectral density properties to integrability and orthogonality.

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.