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.

Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory

“…As we will see shortly, the symmetry-breaking pattern essentially depends on whether N f /2 is even or odd. 23 As an example for even N f /2, let us take N f = 4 with quarks {u 1 , u 2 , d 1 , d 2 }. For nonzero µ q , the Cooper pairing between u and d becomes energetically costly, so the dominant pairing channels are u 1i u 2i and d 1i d 2i with i = R, L. (Note that these condensates are color singlets for N c = 2.)…”

Dirac Spectra in Dense QCD

“…Zero-mode solutions at μ = 0 were constructed explicitly in [71]. According to detailed perturbative calculations [72], the instanton density for size ρ at large μ is given by The answer is No.…”

Banks-Casher-type relations for complex Dirac spectra

“…Therefore we cannot generalize our result to the color-superconducting state of QCD at high density. Presumably the connection between the Dirac spectrum and the BCS gap is more complicated in this case, similar to the situation at low density [3,4].…”

“…For the derivation of the Banks-Casher relation it is essential that the fermionic measure is positive definite [2]. If it is not, as is the case in QCD at nonzero density, ρ(0) is undefined and the connection between ψψ and the (complex) Dirac spectrum is more complicated [3,4]. Here, we consider QCD-like theories at high density (and zero temperature) that have complex Dirac spectra but positive definite fermionic measures.…”