Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases

TL;DR

This study examines how vector interactions and Polyakov loop dynamics influence inhomogeneous chiral phases in the NJL model, revealing that vector interactions significantly alter phase transition nature and eliminate the critical point.

Contribution

It demonstrates the qualitative impact of vector interactions on inhomogeneous phases and the phase diagram, especially the disappearance of the critical point.

Findings

Vector interactions weaken first-order transitions, turning them into cross-overs.

Polyakov loop effects are mainly quantitative, with minimal qualitative change.

The Lifshitz point remains unaffected, but the critical point disappears.

Abstract

We investigate the role of the isoscalar vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona--Lasinio (NJL) model. Thereby we concentrate on phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original NJL model, the presence of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transition gets weakened and eventually turns into a second-order transition or a cross-over, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. As a result, susceptibilities remain finite.