A comment on chiral restoration at finite baryon density in hyperspherical unit cells

TL;DR

This paper critically examines the use of hyperspherical S^3 cells in modeling chiral symmetry restoration at finite baryon density, clarifying their unique properties and addressing misconceptions about their physical significance.

Contribution

It clarifies the interpretation of S^3 hyperspherical cells in dense baryonic matter models, emphasizing their unique features for chiral restoration in Skyrme models.

Findings

S^3 cells uniquely enable full chiral restoration in Skyrme models.

The interpretation of S^3 cells as crystal units without physical significance is insufficient.

The paper suggests further development of the correct interpretation of S^3 cells.

Abstract

Prompted by recent work of Adhikari, Cohen, Ayyagari and Strother "On chiral symmetry restoration at finite density in large-N_c QCD" (Phys. Rev. C 83, 065201 (2011)), we revisit the description of dense baryonic matter in terms of hyperspherical unit cells. We focus mainly on the interpretation of the unique energy, curvature and symmetry properties which enable such S^3 cells to describe full chiral restoration in Skyrme models and which markedly distinguish them from the flat and periodic unit cells of Skyrmion crystals. These key features clarify, in particular, why an S^3 cell interpretation as a crystal-cell model in which the specific cell geometry is without physical significance, as tentatively adopted by Adhikari et al., is insufficient. The ensuing criticism does therefore not apply to the usual interpretation of S^3 cells which we describe. We also suggest a few directions in which the latter interpretation may be developed further.