Inhomogeneous chiral condensates

TL;DR

This paper reviews the concept of spatially modulated chiral condensates at high densities in QCD, discussing theoretical models, phase structures, and the influence of various physical factors on these inhomogeneous phases.

Contribution

It provides a comprehensive overview of the emergence, modeling, and implications of inhomogeneous chiral condensates in QCD at finite density, integrating recent developments and open questions.

Findings

Inhomogeneous chiral phases can emerge near the chiral critical point.

Various models predict different favored shapes and dimensions of modulations.

External factors like isospin chemical potential and magnetic fields influence these phases.

Abstract

The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-$N_c$ approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.