Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density

TL;DR

This paper investigates how two-dimensional large N field theories, specifically the Gross-Neveu and 't Hooft models, develop spatially varying structures at finite density, revealing a Skyrme crystal-like phase near the chiral limit.

Contribution

It demonstrates the emergence of a Skyrme crystal structure in these models at finite density, connecting baryonic matter properties to spatially modulated chiral angles.

Findings

Massless baryons induce translational symmetry breaking.

A sine-Gordon kink chain forms at small quark masses.

Differences between confining and non-confining models are identified.

Abstract

We study two-dimensional, large $N$ field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out.