On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

TL;DR

This paper investigates the possibility of chiral symmetry restoration in large N_c QCD at finite density, demonstrating that spatially varying chiral condensates cannot restore symmetry unless all observables are uniform, through a no-go theorem.

Contribution

It establishes a no-go theorem showing chiral symmetry cannot be restored via spatial averaging in large N_c QCD with non-uniform condensates, extending results from Skyrme models.

Findings

Chiral symmetry restoration via spatial averaging is impossible unless all observables are uniform.

The no-go theorem applies to large N_c QCD phases with non-zero, spatially varying chiral condensates.

Chiral symmetry cannot be restored in models with non-uniform condensates unless all observables are spatially constant.

Abstract

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.