Inhomogeneous Chiral Phase in Quark Matter

TL;DR

This paper reviews the development of inhomogeneous chiral phases in quark matter, emphasizing the nesting effect, topological aspects, and the impact of fluctuations on phase transitions, with implications for astrophysics.

Contribution

It introduces the inhomogeneous chiral phase in quark matter, highlighting the nesting mechanism, topological features, and fluctuation effects, providing new insights into phase transition properties.

Findings

Nesting effect is key to inhomogeneous chiral phase formation.

Spectral asymmetry relates to chiral anomaly and induces spontaneous magnetization.

Fluctuations alter phase transition characteristics via singular propagators.

Abstract

Recent development of inhomogeneous chiral phase in Kyoto group is briefly reviewed. First, the nesting effect of the Fermi surface is emphasized as a key mechanism leading to inhomogeneous chiral phase. After introduction of inhomogeneous chiral phase, some topological aspect is discussed in 1+1 dimensions and in the presence of the magnetic field in 1+3 dimensions. Spectral asymmetry gives rise to anomalous quark number and is closely related to chiral anomaly. It may induce spontaneous magnetization and a novel Lifshitz point may appear on the line $\mu=0$. Some astronomical implications are briefly discussed. Finally, the effects of the fluctuations around the order parameter are discussed; the propagator of the fluctuations exhibits a singularity at finite momentum and changes the properties of the phase transition through loop diagrams.