Inhomogeneous phases and chiral symmetry breaking

TL;DR

This paper reviews the theoretical and model-based evidence for inhomogeneous phases in the QCD phase diagram at intermediate densities, highlighting recent NJL model results with quark-hole condensates.

Contribution

It introduces a 3+1-dimensional NJL model with inhomogeneous condensates, extending previous 1+1-dimensional analyses and revealing novel spectral and free energy features.

Findings

Inhomogeneous condensates can form at intermediate densities in QCD.

The NJL model shows asymmetric spectral density and anomalous free energy contributions.

Results suggest complex phase structures in dense quark matter.

Abstract

In the past few years, a growing number of compelling arguments, backed up by model calculations, pointed out that the intermediate-density region of the QCD phase diagram may be characterized by the formation of inhomogeneous condensates which spontaneously break some of the spatial symmetries of the theory. In the following we provide a brief recapitulation of these arguments and describe some recent results in a 3+1-dimensional QCD-inspired NJL model with quark-hole condensation in the form of a plane wave in the scalar and tensor channels. This model exhibits particular features in close analogy to its 1+1-dimensional counterpart, most notably an asymmetric spectral density and the arising of an anomalous contribution to the free energy.