Dyson-Schwinger Equation and Quantum Phase Transitions in Massless QCD

TL;DR

This paper investigates the stability of the Wigner-solution in Dyson-Schwinger equations for massless QCD, revealing a first-order chiral symmetry restoration transition at moderate chemical potentials and the conditions for color superconductivity.

Contribution

It provides new insights into the phase structure of massless QCD, especially regarding the nature of the chiral phase transition and the absence of competition with color superconductivity at lower chemical potentials.

Findings

Chiral symmetry breaking is stable at low chemical potential.

Chiral symmetry restoration occurs via a first-order phase transition.

Color superconductivity appears only at very high chemical potential.

Abstract

We study the stability of the highest symmetric solution (Wigner-solution) of Dyson-Schwinger equations in chiral limit and at zero temperature. Our results confirm that if the chemical potential is not very large, the QCD vacuum is in the chiral symmetry breaking phase and the quantum phase-transition of the chiral symmetry restoration is in first order. Meanwhile it seems that there is not competition between chiral symmetry breaking phase and color superconductivity phase since the color superconductivity phase appears only if the chemical potential is very large. Moreover, we propose that chiral symmetry breaking arises from the positive feedback with respect to the mass perturbation.