Chiral Spirals from Noncontinuous Chiral Symmetry: The Gross-Neveu model results

TL;DR

This paper demonstrates that in the Gross-Neveu model, the inhomogeneous chiral condensate naturally forms a chiral spiral, revealing how spatial modulations of scalar fields influence pseudoscalar condensates and potentially affect effective theories of quark matter.

Contribution

It shows that the inhomogeneous chiral condensate in the GN model adopts a chiral spiral form driven by scalar density inhomogeneity, with broader implications for effective models of fundamental theories.

Findings

Chiral spiral form of condensate in GN model.

Inhomogeneity of scalar condensate drives pseudoscalar modulations.

Implications for effective models of quark matter.

Abstract

It is shown that the inhomogeneous chiral condensate in the Gross-Neveu (GN) model takes the chiral spiral form, even though the thermodynamic functional depends only on the chiral scalar density. It is the inhomogeneity of the chiral scalar condensate that drives the spatial modulations of the pseudoscalar one. The result has broader implications once we start to think of fundamental theories behind the effective models. In particular, some effective interactions---which may be omitted for descriptions of the homogeneous phases---can be dynamically enhanced due to the spatial modulations of the large mean fields. Implications for the four-dimensional counterparts of the GN model are discussed. In a quark matter context, proper forms of the effective models for the inhomogeneous phases are speculated, through considerations on the Fermi-Dirac sea coupling.